I will enthusiastically, heartily second Heinlein’s “By his own bootstraps”. It is without question the best-written piece of time-travel fiction ever written. Well, at least, ever written up to now; I can’t speak for future works.
Heinlein also did a good job with time travel in The Door into Summer, Time Enough for Love, and “All You Zombies”. Be careful, though: He also did a lot of bad time travel stories. Don’t bother with The Number of the Beast, The Cat who Walked through Walls, or To Sail Beyond the Sunset unless you’re a hardcore Heinlein fan.
Asimov wrote The End of Eternity to prove that he could write good time-travel stories, too. He failed miserably. The best time travel story Asimov wrote was the short “The Red Queen’s Race”.
I haven’t read Crichton’s Timeline, but he tends to research a subject just enough to sound plausible, but not enough to actually be right. What I’ve heard of Timeline seems to confirm this.
Time travel is rather incidental in Carl Sagan’s Contact, but it was a very good book and well worth the reading.
Piers Anthony’s Bearing an Hourglass didn’t do a particularly good job on the time travel front, but it makes for a fun read. I would recommend that you read the series in order, though, starting with On a Pale Horse
The earliest example of time travel was Dickens’ A Christmas Carol, and Mark Twain wrote A Connecticut Yankee in King Arthur’s Court, but in neither of those is the mechanism scientific.
Finally, any story entailing reliable prophecy will wncounter the same peculiar situations as does time travel. The best modern example is probably Heinlein’s “Lifeline”, but the ancient Greeks were also fairly adept at the genre.