GURPS Infinite Worlds

The good news is, we can visit other Earths. The bad news is, somebody out there doesn't like us.

Time Travel combined with alternative world hopping. GURPS: Infinite Worlds is the default GURPS 4th edition setting, loosely inspired by H. Beam Piper's "Paratime" novels. The successor to GURPS Alternate Earths.

The basic concept is this: A Parallel Earth (that calls itself "Homeline") develops the technology for travel to other timelines. It is controlled by the United Nations, which effectively becomes a World Government (an opinion not every nation and corporation agrees with). They secretly explore and exploit the other Earths (in relatively benign ways - buying resources from Earths that have plenty, for example, and dumping wastes on Earths that never developed life) and forms an organization known as "The Infinity Patrol" for the purpose of keeping "The Secret" (that is, the existence of The Multiverse) from those Worlds that do not know about it (the vast majority discovered so far). The reason is because each World is Earth though each is slightly different (or not so slighlty in some cases), and changing it by interfering too much may cause that reality to "shift" closer or farther away from Homeline (that is, it becomes more or less easy to access.) In fact, Homeline's biggest rival, Centrum, a World that also has "cross-time" technology but with a Communist-type socialist technocratic society, seeks to draw worlds "closer" to themselves so they can influence them into developing similar governments. Occasionally, "outtimers" (slang for people from outside Homeline) are recruited to join Infinity if they are judged worthy. This is similar to a Time Police setting genre except it involves parallel worlds instead of the actual past or future. (The book also includes a separate, Time Travel setting called "Timepiece" about people traveling through time via their minds.)

Oh, by the way there's a third up-and-coming player in the multiverse that recently extracted The Secret from a crashed Homeline conveyor. Homeline's name for their timeline? Reich-5.

This setup allows GURPS game masters to permit Crossovers between different genres. For example, the Earth from GURPS Supers has been recently discovered, which could allow for crossovers between the two settings. This also gives both the player and GM a huge sandbox to play with. This is to some degree, the purpose of the setting, as it literally allows the game master and the players to goof around, err.. that is police the infinite multiverse where literally anything is possible (that includes some very weird possibilities) without worrying about actual time-travel (unless you want to of course) The sheer complexity and size of the multiverse and the parachronic physics is probably the main reason The Secret can be maintained with any success at all.

Other tropes

 * Alien Space Bats: Centrum and Homeline do a LOT of this, as often as not as a part of their ongoing conflict. More worryingly, it seems that they may not be the only ones who do this, as Ezcalli and the no less than 18 Gothas (parallels which all suffered a Zombie Apocalypse with a common source) seem to point to...
 * Alternate History
 * Alternate Universe
 * Ancient Conspiracy: The Cabal, which since it's mostly made up of sorcerers and assorted supernaturals with amoral, inscrutable (and often conflicting) goals, is an unwelcome wild card in the conflict between techno-centric Homeline and Centrum. Centrum especially, as their ingrained pragmatism and logic has a hard time coping with a concept as irrational as magic (they tend to pretend it's not there until it goes away, get rid of it by any means necessary if it doesn't, or just pull out if neither option works).
 * Anti-Villain: Centrum really isn't evil, just with alien social values (what we might term "ruthlessness", they term "practicality").
 * There's a section explicitly allowing the GM to decide if they should be A Lighter Shade of Grey or A Darker Shade of Grey.
 * Beware of Hitch-Hiking Ghosts: A double inversion. Troubled people might get picked up by a mysterious stranger who gives them life-affirming advice before dropping them off. Turns out he's some kind of supernatural being (not necessarily a ghost) who drives across worlds for this very purpose.
 * Canon Welding: The 4e version of the setting has absorbed several campaigns from the 3e Time Travel book that were originally entirely separate settings.
 * In a more general sense, just about every other GURPS setting has a corresponding world mentioned in the book. Including the licenced ones (yes, Infinity agents can visit Discworld, Hyboria and Witch World).
 * Crapsack World: Not as bad as most other cases and not immediately apparent, but the more you read, the more obvious it is that there are a LOT more crappy parallel worlds than reasonably nice ones (from the Lucifer parallels to the Reich parallels, with the disturbingly common Gotha parallels and many others in-between), and even the nice ones tend to have ugly caveats - Gernsback, for example, has world peace under the League of Nations (both The Great Depression and World War Two were averted) and awesome Raygun Gothic Schizo-Tech thanks to Nikola Tesla's inventions, but due to not having had those experiences, racism, sexism and colonialism are still firmly entrenched at pre-1940's levels in most inhabitants' minds. It still is one of the most positive parallels overall.
 * Nergal, where the Assyrian Empire destroyed the Hebrews and Phoenicians, prevented the rise of Persia and set a very bloody standard for every empire to follow. Nearly every local culture practices human sacrifice, paper and alphabetic writing disappeared from history, and the world is slowly descending into an anomalous Ice Age that's hinted to be a result of dark magic. It's bad enough that Infinity has decided to throw The Masquerade to the wind; Nergal lacks the technology to replicate parachronics, and to quote the book, "frankly, the Patrol would like to cause as much cultural contamination here as possible."
 * Death World: Several parallels qualify, even appart from the aforementionned Gotha and Lucifer parallels, many of them colloquially called Hell Worlds. The causes run the gamut from incredibly deadly epidemics to man-made ecological meltdown to nuclear war to Alien (or maybe not) Invasion, but probably the most worrisome (i.e. most likely to be completely and irreversibly quarantined) are the (thankfully few) parallels that seem to exist in a Cosmic Horror Story universe.
 * Doing in the Wizard: Inverted, as there are several parallels where magic clearly exists, making it kinda hard to deny. There is even a loose group of powerful magic-users and monsters that also travel through realities, the Cabal (from Gurps Cabal, natch).
 * Enemy Mine: one suggestion in the book is that Infinity and Centrum could ally against Reich-5.
 * Equal Opportunity Evil: Centrum is explicitly called out as finding the concept of discrimination based on race and gender very strange. They're a little more lenient on social divisions, but that's because they're meritocrats.
 * Eviler Than Thou: What is likely going to happen when Centrum and Raven Division finally meet (Centrum are Equal Opportunity Evil meritocrats, while Raven Division...are Nazis.)
 * For Science!: Appart from the Gernsback parallel which plays this straight (if mostly benevolently), there's an interesting variation with the Cabal
 * Grey and Gray Morality: The conflict between Centrum and Homeline, where neither can be easily categorised as pure good or completely bad.
 * The House of Normandy: Where Centrum's history splits off from Homeline's; Henry I's son and heir William the Aetheling doesn't die in a shipwreck, and the Angevin Empire becomes even more of a world-spanning power than real-life Great Britain did.
 * It Got Worse: Many on Homeline in the know consider Reich-5's discovery of parallel worlds to be this; while their own version is, so far, much less performant than that of Homeline or Centrum, it could potentially end up forcing Homeline in a two-front conflict, as the latter's dimensional coordinates are between the other two.
 * Killed to Uphold the Masquerade: Stringently averted by the Time Patrol; Centrum has less scruples, but there are few situations where they'll bother (see just below).
 * The Masquerade: Infinity policy is to not reveal "the Secret" of parachronics to any outsiders, and to actively sabotage anyone else's attempts to do so; people who learn the Secret may be kidnapped and sent to Coventry. Centrum is less anal-retentive about it; they only care if the natives learn about them on planets advanced enough to develop parachronics. However, when that happens, they tend not to let technicalities (like the right to live) get in the way of business.
 * Mental Time Travel: World Jumpers.
 * The Multiverse
 * Multiversal Conqueror: Both Centrum and Reich-5's Raven Division count, for different motives (Centrum thinks they're civilizing alien realities, Raven Division because they're greedy Nazis).
 * NGO Superpower: Infinity Inc. is probably the most powerful entity on Homeline economically and politically.
 * Nice Job Breaking It, Hero: The snafu that resulted in the Reich-5 SS discovering parallel worlds and how to reach them.
 * Reed Richards Is Useless: Averted hard. Parachronics are well on their way to making Homeline a utopia.
 * Aside from China using it to exile Tibetans, that is.
 * Richard Nixon the Used Car Salesman: In what may just be the Most Triumphant Example, the director of the Infinity Patrol's secret ISWAT special task force is... an alternate Otto Skorzeny. However, this alt-Skorzeny was, in his home parallel, a freedom fighter for the multi-national and -denominational, proto-democratic Republican Alliance (in this timeline, european monarchies endured almost unopposed until central-european uprisings in the 1930's), and really, really hates Those Wacky Nazis (especially when they're other hims), and so uses live-fire sabotage missions against them as part of the standard ISWAT training.
 * Spiritual Successor: To GURPS Alternate Earths.
 * Stupid Jetpack Hitler: Reich-5, a world where the Nazis have taken over and developed some superscience. They don't have world-hopping technology yet, but do have some innately gifted people who can do it.
 * Time Police, alternate-history style.
 * Time Travel: But to alternate timelines instead of the actual past or future (unless the GM decides to mix it up), partly to avoid Timey-Wimey Ball-related problems like those nasty temporal paradoxes.
 * United Nations: Though the UN itself is being usurped by Infinity, which essentially doesn't answer to anyone.
 * Well-Intentioned Extremist: Centrum's default moral status.
 * Zeppelins from Another World: The random timeline generation has a specific result that produces these, by the book's own admission (see the quote on that page) driven by Rule of Cool.