Dual World Gameplay

This is when a video game features the concept of the player travelling between two "worlds". It's often done such that you have a normal world and a Dark World, or the player travels through time or a parallel universe. The trope is that the video game will present puzzles and obstacles to the player that can 'only' be solved by travelling between the two worlds.

The gameplay features may vary depending on the choice of justification and developer creativity but there are several common techniques:
 * Having a particular transition point or points to prevent the player from changing too freely (a Portal Between The Worlds, a time machine)
 * Having closed off paths in one world be unobstructed in the other (a wall crumbles away after the years, walls are immaterial in the shadow world)
 * Having directions or objective indicators existing in only one world (demonic markers in the hell world, signs that are still fresh in the past).
 * Enemies only appear in one of the worlds (demons only occur in the demon world, roaming zombies only happen after the Zombie Apocalypse)
 * One world inflicts damage on the player (acidic atmosphere erodes your armour, the bright sunlight of higher realms damages the undead hero)

Video Games

 * In The Legend of Zelda Ocarina of Time, Link can travel seven years forwards and backwards in time by using the Temple of Time. Once you learn some songs, you'll need to return to the past to get some items, and then go back to the future to use them as an adult. Link can also plant seeds in the past to gain access to items in the future, and finish a few other fun sidequests.
 * In The Legend of Zelda a Link To T He Past, Link stumbles across a portal to the Dark World just before what seems to be the final dungeon. This is one of many portals in Hyrule which trap people in the Dark World and warp their bodies. Luckily, Link gets the Magic Mirror right before he enters, and uses it to return to Hyrule. The mirror is used extensively in the second half of the game as Link finds more portals and collects crystals from the Dark World dungeons.
 * Strangely, the Light World has a small effect on the Dark World in a few places, but it's never used extensively.
 * The Legend of Zelda Four Swords Adventures also featured the Dark World, but it didn't cover the entire world. Link could collect Moon Pearls in some levels to open portals, which were used to bypass obstacles and solve puzzles. It came up fairly often, but it wasn't central to the game.
 * Oddly, The Legend of Zelda Twilight Princess averts this trope. The world doesn't change much when it's under the Twilight Ream's influence, but all the NPCs and monsters do.
 * The Legend of Zelda Skyward Sword includes the Silent Realms, areas based on parts of the game world that make you go through a Stealth Based Mission to get needed items.
 * In The Legend of Zelda Oracle Games:
 * In Ages, pictured above, Link learns songs that let him use time portals scattered across Labrynna to travel centuries into the past. It's very integral to the plot, because a sorceress has travelled to the past and is mucking up the timeline. Link has to collect items from dungeons in the past and present in order to defeat her. Later he gains the ability to travel back and forth more freely.
 * The companion game, Seasons, features season-changing gameplay. Every part of the world map is mapped differently for each of the four seasons. Spring makes big flowers grow that shoot you up cliffs, water dries up and vines grow up walls in the summer, leaves cover pits and mushrooms soften in the fall, and water freezes and snow piles up in the winter.
 * Radiant Historia evokes a variation of this trope - instead of separate worlds, Stocke has to traverse two separate timelines, or "Histories". When you meet a road block in the "Standard History", you'll have to seek its solution in the "Alternate History", and vice versa.
 * Eversion actually has more than one layer: there are 8 in total, but per level, you'll only be using 2 or 3 of them. At different layers, different objects may be obstacles or even enemies. In the lower levels, clouds can be platforms. In the highest levels bushes are obstacles, go lower and they are death traps, beyond that they are just dead and background art. Enemies are deadly to different degrees with different one optimised for different levels.
 * Metroid Prime 2: Echoes has Samus travel between Aether and Dark Aether. The planet was split by and the inhabitants of Dark Aether started an invasion. Even worse, Aether is in danger of being destroyed because the Ing stole critical technology from the native Luminoth. Samus finds portals made by the Luminoth that let her travel there to set things right. Because Dark Aether isn't as interconnected, each level's Dark World feels like a claustrophobic, twisted splinter of reality.
 * Oh, and the atmosphere of Dark Aether will eat your suit, just like everything else there.
 * The classic adventure game The Longest Journey did this, in both the original and the sequel, between mundane and magical worlds.
 * The Silent Hill series is probably one of the better-known examples of gameplay involving switching back and forth between a Dark World and a... comparatively normal world, although it generally isn't really under the player's control. One of the newer, not as well received games, gave the player complete control.
 * Trilby's Notes has a normal world/dark world mechanic heavily inspired by Silent Hill -- the player can switch at will to a certain extent and often encountered the "path open in another world" technique, although the Dark World does pop up unexpectedly sometimes.
 * For something rather different in genre, the Raidou Kuzunoha games have a normal world and a Dark World. Switching is entirely under the player's control but can be done only from one place. The Dark Capital is essentially a gloomy and overcast version of the regular capital. There are no people on the streets (normally); it's inhabited entirely by demons. Energy barriers called Dragon Gates block paths that are accessible in the normal version of the Capital, and you can only go between the regular Capital and the Dark Capital at certain shrines.
 * The Dark Capital is useful to you in that it is your main source of demons to negotiate with, which gets you allies in battle. Refusing to visit it except strictly as necessary will leave you underpowered and ill-prepared for the challenges you'll face in the game.
 * It's also necessary to the plot; oftentimes those kidnapped by demons wind up in the Dark Capital, and people harassed by demons usually require the problem to be traced back to the location's Dark Capital counterpart. As a Devil Summoner and a private investigator, that usually means it's Raidou's job (and thus, the player's) to do it.
 * Legacy of Kain: Soul Reaver featured an original take on this with the material realm/spectral plane mechanic: Since the player character is an undead wraith, he is a native of the spectral plane, his energy drains constantly in the material realm (unless he has maximum health, and the titular Soul Reaver on-hand), and losing all of his health kicks him back into the spectral plane, although he can shed his material form at any time. However, travelling back to the material realm requires the player to find a conduit and be at full health. In the spectral plane, time stands still, so the player can't open doors or push or pull items, but with a certain skill they can at least transition through gratings. In addition, the scenery in the spectral plane is twisted and contorted, so what was once an impassable gap in the material realm can turn into a doable jumping puzzle in the spectral plane. The duality factored into the combat as well: The player could find dangerous wraiths in the spectral plane, and revive their bodies in the material realm, where they were even more difficult to fight.
 * Chrono Trigger does this with seven different time periods, accessible via fixed time gates. After you find The Epoch, you can time travel anywhere on the world map.
 * Chrono Cross had parallel worlds too, each from a different timeline. There was only one portal to travel between them, and you had to figure out your own way to navigate the world map in each. Despite being parallel worlds, one side could affect the other e.g. cooling scorched ground on an island in one world allows plant life to grow in the other world.
 * Day of the Tentacle features a novel variation. The three characters are trapped in three different time periods and have to work together, using items from different time periods by passing them through a time-traveling toilet.
 * Prince of Persia: Warrior Within had the Prince moving between the Island of Time's past and present. In the past, he could access rooms that were destroyed in the present and meet characters that were long dead by that time. In the present, he could use the damage to the island to access areas that are normally inaccessible in the past.
 * Master of Magic has Arcanus and Myrror. The latter is a Mirror Universe with other races and more magic. Units can go back and forth via towers, "plane walk" spell and some on their own ability. The goal is to conquer both, anyway.
 * Age of Wonders: Shadow Magic one-ups this by having battles take place in up to three parallel worlds: the Surface world has varied terrain and mimics the real world (albeit with Patchwork Map tendancies), the Underground is a vast warren of caves that restricts movement and visibility for most races (giving an edge to natural burrower factions), and the Shadow world is a bizarre astral plane that allows rapid movement, but inflicts a debilitating shadow sickness on most races (giving a huge combat advantage to units immune to this effect).
 * Spyro: Shadow Legacy pits the eponymous hero against enemies from the Shadow Realm. These creatures are impervious to standard attacks, which makes it easy for them to capture just about everyone; even Spyro himself is initially powerless against them. After undergoing a crash course in new combat techniques, Spyro hops back and forth constantly between the material and shadow planes; some bosses require you to switch worlds multiple times to bring them down.
 * The first stage in the "Milky Way Wishes" part of Kirby Super Star (Ultra) Is a stage with doors leading to the same area, only in a different season. The object was to traverse the stage in the right seasons to bypass obstacles.
 * Prey lets you leave your body temporarily to walk around in the spirit realm. This lets you walk through force fields, kill enemies with arrows, and do some other nifty stuff.
 * In the Opposing Force expansion of Half Life, Adrian Shepherd gets a portal gun that lets him jump between Xen and Earth at any time. This is usually a good idea if you're in a tight spot, because Xen tends to be less hostile than Black Mesa.
 * Usually. This is a unusual example in that you can access Xen from any point by just using the gun's alt fire, but you always return to a fixed point in Black Mesa (varies with the map you're on). What awaits you in Xen varies, from some supplies, a healing pool, to a very, very long drop.
 * Mario & Luigi: Partners in Time is a disappointing subversion. Although the plot revolves around time travel, you don't actually get to explore any of the Mushroom Kingdom in the present. The only time Dual World Gameplay comes up is in The Very Definitely Final Dungeon, where the only way you know where you're going is because you've been through the Castle a few dozen times in the present.
 * Super Mario Bros 2 has the magic potion, which makes a door to a Dark World where you can grab coins and power-ups. You were only limited to the screen you made the door on, so the trick is to find places where powerups are hidden and make the door there.
 * Super Mario 64 features Tiny/Huge Island, where Mario can go through pipes to change size. As a giant, Mario can easily jump up cliffs and doesn't need to worry much about enemies. As a midget, Mario can ride on breezes and enter narrow passages. This is implemented by two different maps of the same island.
 * Super Mario Bros 3 has a similar level, where going through doors shrinks the normally enormous enemies to normal size. The environment remains big, however.
 * Happens strangely in Bowser's Inside Story. In some places, Bowser can do things that change some aspects of his internal workings. If he drinks water, some areas become covered in such, allowing the Bros to swim. Standing in front of an X-ray reveals some passages. And so on.
 * Neverwinter Nights 2: Mask of the Betrayer does this. Things in the plane of shadows are shaped differently than in the material plane. Most notably the small temple of Kelemvor becomes the massive Death God's Vault. You can use portals to the plane of shadow to pass obstacles or find things that don't exist in the material plane, or find people hiding out in the plane of shadows.
 * Final chapter of Naverwinter Nights: Hordes of the Underdark features a ring that shifts you into a parallel world when equipped, which is required to pass some obstacles. Shadows of Undrentide also has a short plane-shifting sequence.
 * Wario Land 3 has a day/night cycle integrated into the entire game, with each level mapped twice for day and night. Many treasures cannot be accessed at the wrong time. During the day, monsters patrol everywhere and doors in cities are open. At night, robots prowl where enemies were, and the hungry dead stalk the dark places. Near the end of the game, you get an item that lets you change the time of day on the world map without having to enter a level.
 * Minecraft has the normal world and the Nether, accessible through obsidian portals when lit on fire. (This is creates an inconvenience in SMP - survival mode multi-player - where having two maps hosted on the same server can be a major memory strain.) The Nether is smaller than the normal world, ten meters in the Nether is eighty meters outside. This makes it convenient for fast travel, assuming you can travel safely.
 * As of full release, Minecraft has a third world, called "The End". It's a floating landmass, full of Endermen and the games only boss. To get there, you need to fix an enderportal, found in a Stronghold (found in the main world), with items obtained in the Nether.
 * The Digipen game Duality.
 * Dragon Quest VI takes place  in the Dream World and the Real World, which look very much alike, and you'll be traveling between them often.
 * Dragon Quest VII has the similar-looking present and past worlds.
 * Mario Party has a few boards that change state. All of the boards in Mario Party 6 undergo a day/night cycle.
 * Happens in The Lake stage in The Subspace Emissary.
 * A variation of the trope is present throughout Sonic Unleashed. Not only do the "dual-worlds" in question (daytime/nighttime) have completely different level designs, but they also have different gameplays between them.
 * Castlevania: Harmony of Dissonance does this. It's a bit of a reveal that the second castle exists though - then you warp back and forth between the two castles. This makes backtracking very annoying, especially before The Reveal of the two castles' natures. Near the end, you have to locate all six of Dracula's relics, hidden away in both castles. You'll have likely found two or three initially though. Where you fight at the end also determines the ending.
 * A subversion in Final Fantasy VI; you never actually enter the Esper world, and only see it in Terra's flashbacks.
 * The X-Dimension stages in Disgaea are... sort of like this. Basically their modified versions of the same stages from the story, but with higher level enemies, geo-block puzzles and occasionally other special conditions.
 * The second game of Boktai features Bonus Dungeon House of Time, where you travel between past and present to advance.

Tabletop Games

 * The Dungeons and Dragons cosmology.
 * Classical version expanded and expounded in Planescape has Ethereal and Astral planes to connect everything else to the Prime (worlds of mortals) and consequently have corresponding areas. Ethereal has Borders, contacting Prime and Inner planes and separated from Deep Ethereal by curtains. Also, shadow mages discern Shadow Fringe -- less dark and dangerous part of Demiplane of Shadow connecting to the shadows in Prime. So, ghosts dwell in the Border Ethereal, invisible but able to see everything in reality within a few feet. When they want to haunt someone or something, they can "manifest" by moving halfway between the planes. Magic users can become ethereal to float through walls, "make a short cut" via Shadow Fringe or move to another plane entirely.
 * 3.5 edition has coterminous planes, which connect at a few points, and coexistent planes, which overlap.
 * Adventure I10 Ravenloft II: The House on Gryphon Hill. If the DM had module I6 Ravenloft, the PCs could switch back and forth between modules, fighting Strahd in both. It's possible for the PCs to find items or information in one world that could help them in the other.
 * Birthright campaign setting. Halflings originally came from the Shadow World but fled to Cerilia when a force of evil corrupted their homeland. They and other Cerilian races can travel there if necessary.
 * Streamlined in 4e, with the Feywild and Shadowfell being the brighter and darker version of the world, respectively.
 * Magic the Gathering has done this a few times, with suspend (exile with counters, removing one during each upkeep, and playing it when they're all removed), phasing (put the card and everything attached to it in a special zone at the end of turn, or whenever it "phases out", only to put it back in play at the beginning), shadow (creatures with shadow cannot block or be blocked by creatures without shadow, seen as another world), and lots of things like Parallax Wave (exile cards temporarily).
 * Exalted has the Underworld, which is a dark reflection of Creation; some necromantic spells allow you to instantly step between corresponding points on the two, and the dark Labyrinth beneath the Underworld also allows it to be used for fast travel. There's many other worlds, like Autochthonia, Hell, or Yu-Shan, but the Underworld is the only one that explicitly maps to Creation.
 * Several of the monster types in White Wolf's Old World of Darkness had access to the Umbra, a spirit world containing a duplicate of the entire world. The Garou in particular were known for jumping into the Umbra to study or fix problems popping up in the physical world.
 * White Wolf loves this trope as an explanation for the creepy crawlies of the gamelines in New World of Darkness:
 * Werewolf: The Forsaken: The player characters are part-human, part-wolf-spirit that can easily sidestep between this world and the Spirit World (called 'Shadow'). Any permanent-ish solution to the world's (Crapsack World many) woes usually need things to be done on both side of the Gauntlet.
 * Geist: The Sin Eaters: The same, but replace Werewolf with Sin-Eaters and Spirit World with The Underworld.
 * Changeling: The Lost: The same, but replace Sin-Eaters with the Changelings and The Underworld with Arcadia. Unlike the Shadow or the Underworld, Arcadia doesn't map into real world. Oh and the Changelings don't consider Arcadia as their turf, either.

Board Games

 * This is the entire concept of a variant of chess called Alice chess. A piece on Board A moves to a space on Board B.