Rollercoaster Mine

"I reckon you're all ready to take a nice, easy tour of this here ol' mine. Ohhhh, they fixed it up real nice and safe for ya, heh heh heh! 'Cept that you ain't goin' there, noooo! You're gonna see MY kinda mine! Ah ha ha ha ha! If you can! Just try and come back alive! Ah ha ha ha haaaa!!"

—Evil tour guide, Devil's Mine Ride

A staple in Western movies along with a couple Adventure films, the Rollercoaster Mine is a mountain railway used as a roller coaster. Mining trolleys roll at high speed down impractically steep and seemingly frictionless rails that weave in and out of an improbably long chain of tunnels, and often across bridges. Sometimes, they'll even do jumps. Works great for a Chase Scene.

Surprisingly often, a mine cart full of protagonists that's been rolling downhill at great speed for a couple of minutes will suddenly break through a nailed-together criss-cross of old boards, and burst out on the surface. If this phenomenon can be harnessed, it will provide the world with infinite energy. Of course, they may have started at a higher altitude, or something.

Theme Park Landscape is the supertrope. Minecart Madness is a Video Game-specific subtrope.

Examples of Rollercoaster Mine include:

Anime and Manga

Possibly the railway chase scene in Laputa: Castle in the Sky.
The Pokémon episode "Island of the Giant Pokemon."

Comic Books

Carl Barks's "Land Beneath The Ground".
- Many other Disney Comics too.

Film

Indiana Jones and the Temple of Doom.
La Ballade des Dalton, a Lucky Luke animated movie .
The 2008 version of Journey to the Center of the Earth has one. Which was in 3-D no less.
Japeth takes Red on one such ride in Hoodwinked.
The 2001 German western parody Der Schuh des Manitu / Manitou's Shoe
Replace the mine cars and tracks with bare-assed sliding through ice tunnels, and you've got the cavern scenes from Ice Age.

Literature

Gringotts Bank in the Harry Potter series.

Live Action TV

Opening titles to the fourth series of Games Master.

Real Life

The Big Thunder Mountain ride in the Disney parks is built around this trope. Indeed, this is a not-uncommon type of roller coaster.
- Cedar Point's Cedar Creek Mine Ride is actually one of the tamer coasters at the park, and favored by riders who aren't quite up to the Millennium Force.
The page quote is from a motion simulator ride called The Devil's Mine which is based on this trope.

Video Games

Reverend Ray has an option of riding a cart in the mine level of Call of Juarez.
Mario Kart Wii has "Wario's Gold Mine," a track set in one of these.
Minecraft allows you to build one of these.
Numerous levels in Donkey Kong Country.
The final challenge in Last Train To Blue Moon Canyon.
This is a recurring level theme in the Sonic the Hedgehog series.
- Sonic 2 for the Master System/Game Gear has Underground Zone.
- Sonic Rivals 2 has Frontier Canyon.
- The last portion of Rocky Ridge in Sonic Free Riders consists of this. Interestingly, the mine carts go faster than the hoverboards they're racing on.
The underground coaster maze in Myst's Selentic age.
- Also, one mode of transport in Riven is by mine cart.
This is a standard type of coaster in Rollercoaster Tycoon. It's not even a themed car style; it's an actual unique ride type.
Duke Nukem Forever has a brief Rollercoaster Mine sequence near the end of its Wild West section.
Dwarf Fortress minecarts allow lots of possibilities, and easily integrate with mechanisms like drawbridges (used as track switches), Pressure Plates, etc. And yes, they can skip through air for a while and land on an unconnected track on the other side of a chasm, etc. Players have set up all sorts of uses and contraptions involving them - from "battle train" tracks (fast patrol with crossbows) to automated magma traps (roller-driven nickel carts scoop magma, then follow a track with dumps over floor grates, triggered by Pressure Plates on a floor below), to "minecart shotgun" (load a cart with a bunch of small dense items or a giant spiked ball, push it down a few ramps ending in a sudden stop against a fortification). Also, it turned out that riding a minecart through several water tiles is one of the safe ways to train swimming.

Web Comics

Deliberately (and emphatically) averted in this Chasing the Sunset strip.
Played straight in Our Little Adventure as the cart Julie and her group rides on does steep drops and even loops. The cart does jumps as well, though this is accomplished with a wand they picked up as treasure earlier.

Western Animation

Hanna-Barbera's The Adventures of Gulliver episode "The Hero". After Captain Leech kidnaps Flirtacia, the other Lilliputians follow him into a mine. They end up pursuing him with both parties traveling in mine carts.
In Tiny Toon Adventures: How I Spent My Summer Vacation, Babs, Buster and company go through a literal example of these, complete with a shopping mall AND the theme park Happy World Land, all while being chased by a Jason Voorhees ripoff with a chainsaw.
There's a brief minecart pursuit in the 1973/74 Superfriends episode "The Planet Splitter" when Doctor LeBob's assistant Wilbur tries to escape through subterranean coal mine tunnels.
Home on the Range has this when they capture Alameda Slim.
One of the Raceworld zones in the Kerwhizz episode "Wild West World" features an abandoned mine, through which the racers are pursued by what they think are bandits in a mine cart.
In the Family Guy episode, "The Courtship of Stewie's Father", Peter is rescuing Stewie from Disney World employees and they hop on an Indiana Jones-themed minecart ride (complete with Peter in Indy's regalia).
My Little Pony Friendship Is Magic has gotten in on the fun, in "A Canterlot Wedding."

"Well I'll be! You made it through! You're the first to come back alive in a long time! Wait...You wanna see it again? Huh?! Ah ha ha ha ha ha!"