Donald E. Westlake’s Smoke.
Westlake’s primarily a crime writer, so the theme is: What if you were a small-time burglar, and you received the gift of invisibility?
Not a book, but a great time-travel story in movie form:
Time Rider. It might be a book…
What about Stephen Baxter’s sequel to Well’s “The Time Machine” - “The Time Ships”? Also the short story “Air Raid” by John Varley (the story he later expanded into the novel “Millennium”.
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IMHO question. Moving.
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Heinlein’s “By His Own Bootstraps” (mentioned above) is without a doubt the best time travel story ever written, and The Door into Summer is also very good. Many others of his novels and stories dealt with time travel (not mentioned yet are Farnham’s Freehold and “Elsewhen”), but I don’t think any of them were as good. Does anyone remember what collection “Bootstraps” was published in?
For historical interest, Dickens’ A Christmas Carol is generally regarded as the first story dealing with time travel, though not in the form it’s most often recognized. In some senses, though, any story involving prophecy (well, ok, accurate prophecy) can be considered to deal with time travel of a sort, and many of the Greek myths do touch on some of the same paradoces which are characteristic of time travel.
Personally, I wouldn’t classify Wells’ The Time Machine as being about time travel at all: There, the Machine is just a McGuffin to transport the hero to another world, like-and-yet-unlike our own. Similar arguments apply to a lesser scale to Asimov’s The End of Eternity: I don’t think that Asimov ever wrote any good time-travel stories, except possibly Pebble in the Sky, but time travel was only incidental there.
And the whole “moderator watch” thing comes (I assume) from John D. MacDonald’s The Girl, The Gold Watch and Everything and/or my swipe of it for Chronos’s origin. 
Also, there’s David Gerrold’s utterly, supremely bizarre The Man Who Folded Himself
Chronos mentioned Heinlein’s “By His Bootstraps” (from the collection The Menace From Earth, but there’s the even more bizarre “All You Zombies” also by Heinlein (found in The Unpleasant Profession of Jonathan Hoag).
Also DeCamp’s masterpiece Lest Darkness Fall has to be mentioned.
Spider Robinson wrote a hysterical story about a malfunctioning time-belt called “Half An Oaf”.
I could go on and on and on. (But, thankfully, I shan’t)
Fenris
I’m coming in late to this conversation, so apologies there but I had to comment on your list - ALL great reads, every one of them, but dang the David Gerrold yarn had staying power for years for me. I read that in 8th grade back in the late 70s. With your reminder, I may have to go find a copy of that and read it again.
The Sound of Thunder. Great story.
The Time Machine Saga was a super fun story by Harry Harrison. It was also called “The Technicolor Time Machine”.
Also jumping in late but I’m surprised nobody mentioned “The Men Who Murdered Mohammed” by Alfred Bester. It has both time travel and invisibility.
Thread moved from IMHO to Cafe Society, which did not exist when this thread was first created.
What about The Ugly Little Boy?
Time and Again by Jack Finney is my favorite time travel book.
Also, isn’t it a law to mention Ken Grimwood’s Replay in these types of threads?
Patton’s Spaceship and its sequels.
The Ivanhoe Gambit and sequels. They kinda go off the rails later on but the first few are quite good, if you like pulp.
The Man Who Folded Himself by David Gerrold is probably the most ‘pure’ time travel novel I have ever read.
Multiple and rapidly increasing timelines and many simultaneous versions of the main character. Highly memorable.
Looking Backwards by Edward Bellamy may be the first time travel novel in history (something like 1888).
Just a touch older than the start of this thread, Hari.
Charles Stross’s Palimpsest won the Hugo for Best Novella in 2010. Excellent treatment of the topic, and incomprehensible for me to understand. Time travel stories give me a headache, but his is well done. His Singularity Sky miniseries (two novels) isn’t about time travel per se, but uses time travel, sort of, in parts. Never violating causality. Lots of talk of light cones.
There’s Niven’s Flight of The Horse stories, where the joke is that time travel is fantasy, so everytime the hapless traveler goes into the past, he gets accosted by mythological creatures. Fun. Not headache-inducing.
Invisibility: The Glamour, by Christopher Priest. Fade, by Robert Cormier. (Both novels)
Time Travel: “The Man Who Came Early” by Poul Anderson. “A Gun for Dinosaur” by L. Sprague de Camp (both short stories).
The Ugly Little Boy
The Dead Past
Blank
A Statue to Father
The Winds of Change
“The Ugly Little Boy” was a good story, and a time travel story, but it wasn’t really a good time travel story. That is to say, while it does include time travel as an essential plot element (more so, I’ll grant, than Pebble in the Sky), what makes it good isn’t the time travel.
“A Statue to Father” is even more so: It’s a joke story that happens to be based on time travel, but the time travel is even more incidental: The portal could just as well have been to a different planet or a different dimension, and it would work just as well.
“The Dead Past” isn’t a time travel story at all. It does do a very good job of exploring the implications of the technology central to the story, but that technology isn’t time travel.
I can’t bring to mind “Blank” or “The Winds of Change”. I’ve probably read them, but I couldn’t say for sure.
Some good time travel stories/novels.
Millennium by John Varley
“‘And It Comes Out Here…’” by Lester del Rey
“Vintage Season” by C.M. Moore/Henry Kuttner (as by Lawrence O’Donnell). From the point of view of people being visited by time travelers.
“Mimsy Were the Borogoves” and “The Twonky” by Kuttner are related to each other, about artifacts from the future sent back in time.