I can think of a few TV shows, but that’s it.
Oops, almost forgot the Back to the Future Trilogy.
Thought of another one Peggy Sue Gets Married.
I’m assuming in your TV shows you’re including Quantum Leap, because … yeah.
Was going to mention Stephen Fry’s Making History, but I honestly don’t remember how that ended.
ETA: Probably lots of examples on this TVTropes page: http://tvtropes.org/pmwiki/pmwiki.php/Main/SetRightWhatOnceWentWrong
Warning: TVTropes page.
Sure there’s plenty. Back to the Future - Before his trip, Marty’s family was very unhappy, had crappy jobs, a terrible boss. Afterwards, they were wealthy and very happy.
*Peggy Sue Got Married *- IIRC Peggy falls in love all over again, fixes her relationship with her sister, and wakes to what may be a better future.
Twain’s Connecticut Yankee in King Arthur’s Court as I recall, he did a lot of good while trying to get back home.
Source Code, sort of.
Dejavu, sort of.
Somewhere In Time led to finding true love, so that’s sort of good.
The Butterfly Effect showed a number of positive and negative effects of travel to the past, but the ultimate ending is a good result (if not ideal) from the time travel.
There’s “A Sound of Thunder”, if you voted for Deutscher.
Nitpick: if you consider killing 30,000 people “a lot of good,” sure, okay.
Time and Again by Jack Finney.
Mib 3.
Star Trek IV
Saved the whales
The old series Time Tunnel is a distant childhood memory. I’m pretty sure at least a few of those episodes had a positive outcome.
Theme song
Star Trek: First Contact, in which they save the Earth from being taken over by the Borg (who, technically, went back in time to do it, so they probably cancel each other out…).
City on the Edge of Forever, going back in time prevented the Third Reich from taking over the world.
But that was just to un-do McCoy going back in time and bringing about the Third Reich taking over the world in the first place. 
Millennium, the John Varley book (and movie). People from the future take doomed people from the present to repopulate the Earth in an even further future.
Bill and Ted’s Excellent Adventure
The Anubis Gates, by Tim Powers, in which a guy goes back in time and becomes Samuel Taylor Coleridge, noted poet and laureate.
Not quite - He meets Coleridge but he becomes William Ashbless
It’s been a while. I do see a trend in which people go back in time and seem to profit, but really, they’re just cleaning up a mess (their own, or somebody else’s).
Heinlein’s Lazarus Long stories… in which (in Time Enough for Love), Lazarus goes back in time so he can have an affair with his mother, then (in The Number of the Beast) brings her forward in time (saving her life in the process (actually, it’s some very distant descendants of his, including a couple female clones of himself) to join the Time Corps, and she eventually (in To Sail Beyond the Sunset) goes back in time so she can … “recruit” her father.
Not exactly time travel, but it does involve getting a message from the past: Frequency.
Terminator 2 stopped Judgement Day and then they never made any sequels
If we take Terminator at face value along with the deleted scenes, and ignore the sequels.
Reese going back in time lead to the human race being saved, both through his er personal contribution and the information he imparted to Sarah which she then imparted to John.