Avoid the shit movie by all means but do read Timeline by Michael Crichton.
Very entertaining fast read.
Let me get in another plug for Varley’s Milenneum. The novel is excellent–one of my all-time favorites. The movie…not so much.
Tunnel Through Time by Lester Del Rey is a great book. Basic plot: a physicist invents a time machine and sends a paleontologist back the age of dinosaurs. But he doesn’t come back on schedule, so his son and the physicist’s son go back to search for him. What I like about the book is that these people aren’t a bunch of idiots geting chased by dino’s; they know how to take care of themselves and bring the necessary equipment along, like high-powered rifles and .45 automatics, and survival gear.
Due to an accident involving a brontosaurus, the time machine is damaged, and the team can only make it back to the present in short hops. So they end up successively getting chased by T.Rex and Pterodactyls in the Cretaceous, almost freezing to death in the Ice Age, and getting caught up in tribal warfare in the Pleistocene. There’s enough character development to make you really care about the people, and you may even shed a tear or two at the end of the book as you contemplate the unknown fate of the little cave girl G’na.
Anyway, I highly recommend it.
I came in to say Connie Willis, but I was beaten to the punch, so I’m seconding that.
“The Man Who Folded Himself” is really the ultimate time travel novel/novella.
You know the time travel cliche where a future version of yourself comes back to advise you about an action you’re about to take? Well, if you had a working time machine, wouldn’t you experience this just about every day?
I recommend *The Light of Other Days * by Stephen Baxter and Arthur Clarke. It makes time travel not only realistic, but inspiring.
For a really different method of time travel (but, if it works, one that every one of us has tried – unsucessfully, but it did have other pleasures), see Ray Nelson’s “Time Travel for Pedestrians” in Again, Dangerous visions 
Pastwatch: The Redemption of Christopher Columbus by Orson Scott Card is about an attempt to change history by going back to Columbus’s first meeting with the natives of the New World.
by Keith Laumer.
That’s fairly recent, right?
The origin of the cliche mentioned in the OP is A Sound of Thunder by Ray Bradbury. A nice, complicated, time travel story is The End of Eternity by Isaac Asimov. Not one of his best, though.
Poul Anderson had a series on the Guardians of Time. Jack Williamson’s Legion of Time was the first instance of a corps of time travellers fixing problems. The Men who Murdered Mohammed by R. A. Lafferty is a reasonably plausible one. The most realistic one I know of is Timescape by Greg Benford. Time communication, not travel, but I found it quite gripping.
I favor the Heinlein stories already mentioned, as working out all the implications in two great stories.
I haven’t read it yet, but if it’s as good as his other books, I feel safe recommending A Shortcut in Time by Charles Dickinson.
I second or third the recommendations for Replay and Doomsday Book. Green Darkness by Anya Seton might be dated (lots of 70’s references) but I loved it way back when.
Also read Time and Again and its sequel From Time to Time. I loves me some Jack Finney!
Alfred Bester, not Lafferty.
There’s also George Alec Effinger’s novella, “The Bird of Time Bears Bitter Fruit.” He expanded the idea into The Bird of Time, which I haven’t read.
Oh, I forgot, Michael K. Swanwick wrote one fairly recently called, I think, The Bones of the Earth that was really good (if a little muddy at the end.)
There is a series of books by Kage Baker that has to do with time travel. They’re called the Company series, but are better known by their individual titles. The first one is In the Garden of Iden. The time travel is more a plot device than the point of the story, but the series is still very, very good.
The Technicolor Time-Machine by Harry Harrison is a good fun read. In it, the time machine isn’t used for jurassic hunting trips or to solve historical mysteries, but for a much nobler purpose: to make a Viking movie!
Anyone with me on loving that Choose Your Own Adventure book called The Cave of Time?
I remember that one! And another where a group of dinosaur hunters return to their own time and find it’s all changed - because one of them stepped on an insect in the past.
And some more - another Biblical one, Let’s Go to Golgotha by Garry Kilworth.
And the veteran British SF writer John Wyndham (who wrote Day of the Triffids) did a short story called, I think, Chronoclasm.
Also the British SF humour writer Jasper Fforde’s literary detective Tuesday Next does a lot of time travelling with her dad. Quote: “My father had a face that could stop a clock …” (literally!)
There’s this really great novel that’s going to be published next year, and …
Crap, I’ve said too much!
Can you remember what it was called? I read it in a book of “comic” sf and fantasy, which I have since lost. Always remember that story as being rather grim and glory.