Faster than light travel
This one is simplest for the author, and interferes least with the plot. For those reasons, it's popular in movies where there's limited time to spend on exposition. Star Wars is an obvious example: When Luke Skywalker wants to go visit Yoda, he just hops in his spaceship and hits the gas. Iain M. Banks uses this in his Culture series. It's great for space opera and other "soft science fiction" writing, where the author doesn't want to swamp the action in elaborate lies about physics.
The passengers and crew of a ship are put in suspended animation for the duration of the trip; see Orson Scott Card's The Worthing Saga for one example, and the three Alien movies for another. In the first of that series, Alien, cold sleep was not merely depicted, but used as a plot device. That was cool. In fact, cold sleep is often used as a plot device, because it's both creepy and seriously obtrusive.
James Blish chose immortality for his Cities in Flight novels: It takes a hell of a long time to get there, but they've got time to spare. This isn't necessarily much use in a movie. There's not much to say about it, either: People get real old. They don't die. They get even older. They still don't die. Yeah, yeah, yeah. Next?
It takes a hell of a long time to get there, but they're travelling so fast that relativistic effects kick in, and the subjective transit time experienced within the ship is relatively brief. Those on the space ship might age two years while those on the planets of departure and destination age fifty. Vernor Vinge's A Deepness in the Sky is an example (with cold sleep thrown in too), or Robert Heinlein's Methuselah's Children (which also involves very long life spans, though no actual immortality). Then there's Orson Scott Card's Ender novels, wherein time dilation figures prominently1.
If you want to try to explain this one to an average movie audience, you're welcome to try. Nobody in Hollywood has given it a shot, as far as I know.
A couple of classic examples would be The Stars My Destination by Alfred Bester and Tunnel in the Sky by Robert Heinlein. Necromancer by Gordon R. Dickson pops into my head as well. Oh, and how could anybody forget John Carter, Warlord of Mars, in Edgar Rice Burroughs' classic Mars novels? John Carter just walks out into his back yard in Virginia, spreads his arms, and *poof!*, he's striding manfully across the soft carpet of ochre vegetation on the floors of the dead seas of ancient and fabulous Mars!2
There are variations on this one. Sometimes they do it by massaging their temples and vanishing; sometimes they use a machine. Still, both of those have a very high "bullshit factor". The super-duper magic-handwave nonsense in Card's Xenocide and Children of the Mind is a depressing example of how bad the bullshit factor can get when an author paints himself into a corner with the plot.
Some less blatantly wish-fulfilling ideas involve "loopholes" around the speed of light problem, such as wormholes, or other phenomena dreamed up for the occasion. Larry Niven and Jerry Pournelle invented a handwave called "tram points" for The Mote in God's Eye. Good hard science fiction writers that they are, they made the plot (not to mention the whole history of the galaxy) hinge on it. The idea is that there are certain points in space, near stars, which have a peculiar property: If you approach them at just the right speed, from just the right direction, you vanish and pop up someplace else. They never use the word "teleportation", you see, so it's still "science"!
The space ship is large enough (miles long) to support a self-sufficient population with adequate genetic diversity, farming, etc. The characters don't get there alive: Their descendants do. This would have caused plot problems in Star Wars, for example. "Generation ship" stories tend to focus on the trip itself, usually a small segment of it (e.g. Orphans of the Sky), but sometimes the whole journey from soup to nuts (Mayflies by Kevin O'Donnell, Jr. is a mind-blowing example of this, if you can get your hands on a copy).
This is a classic, classic science fiction gimmick. It's been done and done again, from Heinlein's Orphans of the Sky to Clarke's Rendezvous with Rama, and the prenominate Mayflies (which ought to be better known; read it if you can find it). Gene Wolfe has done a whole series on it, something about "The New Sun" or something. Personally, I find Wolfe unreadable. Then there's Eon by Greg Bear and Lovelock by Orson Scott Card and Kathryn H. Kidd (cough up the damn sequel, Orson!).
I hope I didn't miss any.
. He concedes that the distinction is a subtle one.