Raging Bull: A boxer gets mad at his brother, his wife and/or himself.
Rain Man: A yuppie simultaneously exploits and bonds with his savant brother.
Raising Arizona: An infertile couple kidnaps a baby quintuplet, and they realize that it was probably better if they didn't. They meet up with two escaped convicts, an asshole father and a hairy motorcycle-riding bounty hunter. The feel-good movie of the year.
Ready To Rumble: Total geeks help an over-the-hill athlete get back on his feet, and inadvertently destroy the very franchise they're supposedly promoting.
Real Genius: A bunch of nerds play practical jokes on each other and their professor, though the latter quickly becomes Serious Business. With the help of a super-smart hermit and copious amounts of popcorn, they save the day.
Real Steel: Pre-teen bonds with his estranged father by having his new toy regularly beaten.
Rear Window: A reporter solves a murder mystery without leaving his apartment.
[REC]: A bubbly TV reporter and her cameraman shadow two firefighters to do an episode of their show; but when the firefighters go answer a call, everybody ends up quarantined and Zombies (or some sort of, anyway) ensue.
The Red Violin: Samuel L. Jackson has had it with this motherfucking stringed instrument at this motherfucking auction.
Room: A woman becomes increasingly desperate after being stuck with a small child for a long period of time.
The Room: A film about a man whose fiance has an affair with his best friend. It is poorly acted, poorly written, poorly filmed and the guy who made it gets very annoyed when certain people badmouth it.
Rugrats Go Wild!: People get lost on an island and meet people from another TV show.
Rumble Fish: A street punk learns from his big brother that fighting is wrong, and that he should really relax and go see the world.
Run, Lola, Run: To get some money to her boyfriend, a girl runs and screams. We see the whole thing three times.
The Running Man: Man with peculiar accent participates in hit reality show.
Or... Man with peculiar accent wins Game Show by sending some old guy from Hogan's Heroes hurtling to his death. Somehow this saves the world. Arguably increased audience interest in Japanese reinterpretation of hockey.
Rushmore: An overachieving student likes his teacher; admires/dislikes/envies local industrialist.