Handcar Pursuit

In old comedy films and some classic cartoons, when a scene involves a railroad, there is a chance of a handcar pursuit where one of the character chases another character, also in a handcar usually, by operating a handcar. Usually gets ridiculous when the handcar is able to catch up with a locomotive or is being chased by one.

Compare Racing the Train.

Anime

 * Pokémon: Best Wishes has this involving a subway. Justified that they were able to keep pace, however, because instead of operating it by hand they were using Electric-type Pokémon to power the cars.

Comic Books

 * Tintin (Comic Book) does this in Tintin in the Land of the Soviets. The handcar breaks just as he is about to catch up.

Film

 * The Villain
 * The Crown of the Russian Empire (a Soviet action movie) has the heroine chasing a train on a handcar. She catches up (justified, because it's The Roaring Twenties and the train's locomotive is a steam one).
 * However later the villain they've been chasing unhooks the last train car (yes, while the train is moving) with an oil tank on it, and shoots it, causing it to explode. The heroine passes through the resulting fire on the same handcar (and, apparently, through the wreckage of the car itself, although it could've been blaste off the railway).
 * Buster Keaton in The General.
 * Handcars form part of the chase scene in The Great St Trinian's Train Robbery.

Live Action TV

 * Dads Army: The climax of "The Royal Train" involves Hodges on a handcar chasing a runaway train with the platoon aboard, so he can throw them the widget they need to stop the train. Then they throw the train into reverse, and it becomes Hodges on a handcar fleeing a runaway train instead.
 * In the Loretta Lynn episode of The Muppet Show, a mix-up leaves Kermit and Gonzo stranded miles from the train station where the show is temporarily set, and they travel back by handcar. At one point they get chased by a locomotive

Video Games

 * One of the micro games in Wario Ware Touched. Complete with being chased by another handcar, Wario in his car and a train respectively for the different difficulty levels.
 * Twisted too; it's the boss game for the Dribble & Spitz stage.
 * A recurring team mini-game in Mario Party is a race between two handcars, where you have to coordinate with your partner to speed up, slow down, and bank around sharp corners.
 * The climax of the western world in Tiny Toon Adventures: Buster Busts Loose has Max and Buster escaping from an oncoming train on a handcar ... which reaches 88 mph.
 * The arcade game Magical Truck Adventure is all about this; two plucky kids try to get a magic stone that can transport people between dimensions away from a pair of crooks, and the two groups end up chasing each other in handcars through various other dimensions(all of which inexplicably have train tracks) as they try to get their hands on the stone. The game even comes with custom handcar pump controls.

Western Animation

 * Looney Tunes
 * Ruby Gloom, "Last Train to Gloomsville Part 2".