Hot Tub Time Machine: Three friends and their twenty-something tag-along are blasted back in time to the 1980's when the hot tub at their hotel malfunctions. They decide they need to do everything they did back in the day, so as not to destroy the future. But it wouldn't be a fun movie if they didn't screw up. The squirrel steals every scene he's in. Even the ones with Clark Duke (who's hilarious BTW). And Rob Cordry gives an under-rated and excellent performance.
Terminator: Robots from the future send a cyborg back to the past to kill resistance leader John Connor's mom, Sarah, before he's ever born. The old-school low budget special effects are pretty awesome, and Arnold Schwarzenegger proves that before he was the Governator, he was actually contributing to society by making kick-ass movies. And Linda Hamilton is pretty bad ass as Sarah Connor. Not as bad ass as Ellen Ripley from the Alien movies, but still pretty good.
Donnie Darko: Equal parts teen angst drama, crime mystery, and time travel mind-bender, Donnie Darko is hard to nail down in one sentence, so I won't even bother. I will say that it's completely engrossing, creepy as all get-out, and actually kinda sweet. Jake Gyllenhaal's awkward, uneasy Donnie perfect fits into this movie's off-kilter aesthetic. It's a hard movie to figure out the first time through, so I suggest multiple viewings.
Looper: Joseph Gordon-Levitt plays a thug who assassinates people a big crime syndicate sends back from the future. Things aren't so bad. He even gets to use the future version of a blunderbuss (had to get that word in). Then, his future self (Bruce Willis) shows up on a mission to prevent the death of his wife. Time gets all twisty, Emily Blunt packs around a shotgun and looks hot doing it, and a little kid may be the key to it all. JGL has never been more badass and Willis gets to display the vulnerability that makes him more than the average action star.
The Time Machine (1960): This one's a stone-cold sci-fi classic, based on the H.G. Wells masterpiece. Rod Taylor finds he can't stops his love's death by time-travelling to the past, so he heads for the distant future. He winds up in a far-flung time where he helps the peaceful Eloi battle the monstrous Morlocks. The special effects still hold up today, and the idea of travelling to a new time to forget old heartache is very appealing.
Safety Not Guaranteed: Hard to choose between this one and About Time for the quirky romantic comedy on this list, but this one wins out because I can really relate to Mark Duplass's character, Kenneth. Kenneth's a weirdo who's kind of out of place where he lives. His relationship with Darius (Aubrey Plaza) is completely believable. I mean, I'd fall in love with Aubrey Plaza. Plus, this may be the only movie on this list where we're (possibly) seeing the results of a trip back in time, rather than the trip itself.
12 Monkeys: Based on the French short film La Jetee, this film sends Bruce Willis back in time from a devastated future world to gather information that will help prevent a worldwide holocaust. In the process, he meets whacko animal lover Brad Pitt and a lovely psychiatrist played by Madeline Stowe. This is a Terry Gilliam (the dude who made Brazil) movie, so the visuals are amazing, and Willis gives the best performance of his career. The ending is sad, but inspiring, in a way. To say any more than that would give it away.
Back to the Future: A classic. Marty McFly (Michael J. Fox) takes a trip back to the 1950's and accidentally disrupts history when his mother falls in love with him. Marty has to get his folks to hook up and then get back to 1985, with the help of Doc Brown. The characters are awesome. The action is hilarious. The car is super cool. And, we also get to see how rock and roll was born. You can't ask for more than that!
So, that's my list. What's on your list? What did I leave out? Let me know!