That's why I'm so excited about the film adaptation of Audrey Niffenegger's The Time Traveler's Wife, which tells the story of Henry DeTamble, a man with a rare genetic disorder that causes him to skip around in time while his long-suffering wife, Clare, waits for him at home. The premise is no more or less plausible than that of, say, Back to the Future, in which a tricked-out DeLorean must reach 88 mph to jump into the past. But The Time Traveler's Wife follows through on its premise in a realistic way.
So what are these realistic ways that the movie actually followed?
In a rule-abiding time-travel narrative, there are no parallel universes—just a single timeline. The Time-Traveler's Wife follows this rule to a T, and there is a significant online presence dedicated to diagramming the unique, entangled history of Henry and Clare.
The time-machine construction clause is one of the most often overlooked of the rules of time travel and is the only real mar on the otherwise exceptional Terminator (1984), which proposes a single historical line (or loop) with no alternate universes. (Subsequent movies in the series revert to the parallel-histories model.) The Time Traveler's Wife very nearly gets it right: Since Henry is the time machine, he can't visit any time before he was born. His daughter, on the other hand, bends those rules slightly: She manages to visit a time before her own birth but not so far back that her father hasn't been born, either. (We might take Henry's birth as the "invention" of time travel and the whole family as components of a single machine.)
So, try as you might, you can't kill your own grandfather, nor can you change history at all. The Terminator learned this the hard way, going back in time to prevent John Connor's birth by killing his mother. When a human travels back in time to protect her, the two fall in love—and she becomes pregnant with … John Connor. Ta-da.
There's no need for such finagling in The Time Traveler's Wife. Since Henry DeTamble serves as his own time machine, there's little chance of his preventing his own birth. Cf. rule No. 2.
In The Time Traveler's Wife, Henry and Clare enforce the (predetermined) future by giving each other instructions and hints about how things are supposed to happen. That gives them a feeling of free choice where none really exists. In a letter to Clare about their future, Henry explains, "I won't tell you any more, so you can imagine it, so you can have it unrehearsed when the time comes, as it will, as it does come."
Yes, folks. There are constraints if you want to use physics as the realistic foundation to time travel. And of course, this is assuming that what we know about General Relativity is actually perfectly valid.