Underside Ride

A character hitches a ride by clinging to the underside of a vehicle. This can be done as a means of tailing someone who has their own vehicle when you do not and you cannot risk losing them, or as a means of infiltrating (or exfiltrating) an enemy compound, dropping off the vehicle once you are through the gates.

Do Not Try This At Home. There are a lot of moving parts underneath a vehicle that can chew up a human body real good. And if you fall off - and you will - not only will you hit the road at high speed, you stand a good chance of being run over by the very vehicle you were riding on.

Anime and Manga

 * In Baccano!, Rachel temporarily travels underneath the Flying Pussyfoot train after escaping from the captive diner car.

Comic Books

 * Lucky Luke: When a train is derailed, it's revealed a tramp was travelling on the axles.
 * The Punisher does this at least once to follow a gang.

Film - Animated

 * The Rescuers Down Under. Bernard, Miss Bianca and Joey get under McLeach's truck to follow him when he goes after Cody.
 * Pinocchio. Jiminy Cricket hitches a ride on the coach that takes children to Pleasure Island.
 * This is how the title character in Banjo the Woodpile Cat goes to the city.
 * Toy Story 3 too, IIRC.
 * In Bolt, this is the means by which Penny and Bolt infiltrate the lair of their show's Big Bad. It is reprised a few times throughout the film in different contexts.
 * At the very beginning of Cars 2, Finn McMissile actually clings to the underside of Tony Trihull with his magnetic tires in order to sneak into the Lemons' oil rig.

Film - Live Action

 * In the 1992 version of Cape Fear, Max Cady ties himself to the bottom Sam Bowden's car, causing the Bowden family to take him directly to the houseboat.
 * Fatal Instinct. This comedy parodies Cape Fear (among others) and at one point Max Shady hangs onto the underside of a vehicle while it drives along. When he gets out, it's revealed that friction with the roadway wore through his clothing, exposing his buttocks.
 * The Expendables did this one, IIRC. All I know for certain is that one character is sent on a small cart with an electromagnet (or similar device) to attach something to the bottom of a trailer on a moving truck.
 * The Art of War: Happens near the end, when Shaw (Wesley Snipes) escapes from a group of assassins by lying flat in the road, seemingly to avoid being hit by an oncoming truck. When it passes, he's nowhere to be seen, until it's revealed he escaped by grabbing on to the undercarriage.
 * The ending to Big Trouble in Little China shows the hero happily driving away, only for a last minute Jump Scare revealing a monster hiding under his semi trailer.
 * In Hanna, the main character does this.
 * Jim West in the Wild Wild West movie does this, using a cart designed to let him move between the train they were on, and a chase train. Unfortunately, the rope connecting him breaks.

Literature

 * In The Odyssey, Odysseus and his crew are trapped within a cave by Polyphemus, a man-eating shepherd cyclops. Odysseus and his crew escape by clinging to the underside of Polyphemus' sheep.
 * In the first Splinter Cell novel, Sam uses this trick to get around in Iran.
 * In the Halo prequel novel The Fall of Reach, John and his squad of saboteurs infiltrates an enemy base using this method. The gate guards were Genre Savvy enough to scan the underside of their vehicles with a mirror-on-a-stick. Having none of that, they brought their own mirrors to reflect an unoccupied portion of the underside back at the guards. The kicker was that this was a training exercise, and the Spartans did this when they were fifteen.
 * In Terror Valley by J. T. Edson, Calamity Jane sneaks out of the mission by hiding in a 'possum-belly'; a sheet of rawhide attached to the bottom of a wagon for carrying firewood.

Live Action TV

 * MacGyver: Mac clings underneath a truck to escape the cops in the episode "Jerico Games".
 * In the Burn Notice episode "Besieged", Fiona attaches herself underneath a fuel tanker in an attempt to infiltrate a Right-Wing Militia Fanatic compound. She has a harness spefically designed for this purpose.
 * In one CSI episode, a woman tries to escape from a prison in this way and suffers Ludicrous Gibs from getting caught in the moving parts..

Western Animation

 * Sideshow Bob does it the The Simpsons episode "Cape Feare" in a parody of the scene in Cape Fear.
 * The magician does this in Frosty the Snowman on the underside of a train, in an attempt to get his hat back.
 * Avatar: The Last Airbender: This is how  gets inside Zhao's compound, during "The Blue Spirit" episode, by hiding beneath a layer of dirt in the road. Then grabbing the undercarriage of a supply wagon as it passes over him. It takes him straight inside the fortress.

Real Life

 * One Darwin Award winner tried this while attempting to diagnose a truck's engine, apparently to watch the engine while it worked. It seemed a fine idea until the moving parts caught his sleeve...
 * Jeffery Manchester became the only person to escape from the Brown Creek Correctional Institution by holding on to the bottom of a delivery truck.