A stock plot: the characters have to proceed from a starting line to a finishing line under some set of rules over the course of an extended period of time - often several days. This could be by car, by horse, by foot, or by any means necessary. Expect Badasses of whatevertypesareappropriate.
This may involve Wacky Racing or it may not: the distinguishing characteristic of an Epic Race is the extreme length (generally 12 hours or more), not its idiosyncratic nature. An Epic Race is so long that the challenge of merely going that distance in the time adds interest, irrespective of anything else.
Generally a subtrope of The Big Race, for obvious reasons.
Death Race, an In Name Only remake of Death Race 2000. In this case, it's a NASCAR-style track race where part of the goal is to kill the other racers. Death Race 3 changes the race to a Baja 1000-inspired desert rally.
Arguably, the various Top Gear Specials, although (except for the Polar Special) "get there first" was not the challenge. That said, more traditional Epic Races have appeared on the show: the economy race from Basel, Switzerland to the Blackpool Illuminations took 17 hours; and the car vs. public transport race from Heathrow to Oslo took still longer.
The sport of endurance riding, which involves trekking great distances on horseback. In older times, these races could be cross-country. Nowadays, most national events are between 50 and 100 miles, which can be completed in about 12 hours by the winners. The rides are divided into different legs, with health checks for the horses and riders before they're cleared to continue the competition.
Stephen King, writing as Richard Bachman - The Long Walk. It's a foot race run by 100 teenage boys, the so-called "walkers", with the following rules: if you drop below 4 miles an hour, you get a warning. Receiving 3 warnings in quick succession gets you killed. And as a final touch, it has no finish - it lasts until there's only one surviving walker. It's written by Stephen King - were you expecting a happy ending?
The 1925 serum run to Nome, also known as the "Great Race of Mercy," was not a race against other competitors, but a race against nature itself - 20 mushers and over 150 dogs undertook a 674-mile journey in blizzard conditions to save Nome, Alaska from a diphtheria epidemic after aircraft proved unusable. The serum arrived in five and a half days, a feat that has never been duplicated. The Iditarod, mentioned above, is in part a commemoration of this last great hurrah and Crowning Moment of Awesome of dog-sledding.