There was a short-lived series called Journeyman, in which a guy started popping into the past and figured out he was intended to fix stuff that had gone wrong, or make sure the right things happened.
Well, if Sawyer never went back in time, he never would’ve hooked up with Juliette, and that was a good thing.
I haven’t seen it in a while, but I seem to remember Time Cop having things work out for the better.
Also, a book called Time Craft, where a woman travels back in time several centuries to rescue her parents; however, they were of course there as a result of earlier time travel, so I’m not sure if that cancels it out.
What about Harry Potter and the Prisoner of Azkaban… since we learned they didn’t really change history so much as fulfill it, I guess that one doesn’t count as well.
OK, maybe I don’t have any good examples after all.
For that matter, Quantum Leap. At least, things worked out better (usually) for the people Sam helped, anyway.
I think Heinlein’s story “By His Bootstraps” also qualifies. The protagonist ends up much better than he starts out, by virtue of backwards (and forwards) time travel.
A Swiftly Tilting Planet: by going back in time, history is altered so a dictator doesn’t start a nuclear war.