
Wormholes

This indeed solves a lot of problems. It counters the physical objection, because you can have a wormhole where objects are not moving at the speed of light inside the tunnel, although they might appear to be to outside observers (a wormhole is not simply two black holes with a bridge between them, but rather a black hole and a white hole linked by negative energy).
The show Sliders made heavy use of wormholes and the Einstein-Rosen bridges between them. Wormholes also take care of my main logical objection, the Tourist Trap, which was that if time travel is possible at one point, it becomes possible simultaneously throughout the time stream. Scientists have postulated that time travel through a wormhole would require the “stationary end” to appear first. In other words, a wormhole couldn’t open up allowing you to travel back to someplace where there wasn’t a wormhole before. The point of this being that we may not have experienced time travel yet because the first “stop,” or the first wormhole, hasn’t been created/found yet.
Worldlines

There has been another use of time travel in fiction that I haven’t mentioned yet, but that I have found to be very effective. This is the idea of the worldline. Worldlines are essentially lines that travel through space and time at once, as opposed to a timeline that simply marks the passage of time. In other words, a person’s life, drawn on a graph, would be a worldline, as it plots their movement through space and time. Some time travel stories intimate that it is possible to travel back and forth on your own worldline, since it is simply a line that exists in the universe, not something that is being created or destroyed. Under the right circumstances you should able to walk back and forth along it like the path to your tomato garden.
Whatnot

Star Trek

Quantum Leap, Watchmen, Slaughterhouse Five

I lump these together because they all make what I think is effective use of the “Worldline” theory of time travel. Dr. Sam Beckett can only travel back and forth through time within his own lifetime, while Dr. Manhattan experiences different times in his life simultaneously. Billy Pilgrim has come “unstuck” in time, and experiences his life randomly through time, jumping from one point to the next without rhyme or reason (or at least without rhyme). In each case, the universe is not offended by their time travel.
Back to the Future

Sliders

Comic Books
Members of the Legion of Superheroes travel freely back and forth through time with little concern about the consequences. The mainstream DC universe has not created a very sophisticated look at time travel although they used to have an interesting conceit where if you went back to a time where you already existed, you would appear as a wraith, since the same person cannot “be in two places at once.”

The Terminator

Okay. I’m finally done with the time travel stuff. Next week I’ll go back to ranting about traffic patterns in L.A. or bad poker beats or why some Right to Lifers are psychotic or whatever.