The Cassandra project was in really bad shape when FB open sourced it, and it languished like that for several months before Jonathan Ellis picked it up and ran with it. Now it's a thriving Apache project, with contributors from many companies, and even commercial support through DataStax.
Yeah. My favorite example is JS-2 mode[1]. It's a brilliant mode for editing JavaScript released by Steve Yegge. However, it had some shortcomings and (minor) bugs; Yegge did not have time to support it any more.
Then somebody cloned it on GitHub[2], changed the indentation, fixed some bugs and added some features. In the past, using JS-2 mode was a bit of a compromise--intelligence at the cost of weird behavior. Now there is no compromise at all.
Miranda IM (nee Miranda ICQ) didn't become usable or popular until after I gave up on it. I think it's been abandoned at least once again. Several complete different sets of people have been working on it.
Do you also count partly finished projects? I listed some projects [here](http://news.ycombinator.com/item?id=3713240). Most of them were extended/improved a lot, e.g. by porting them to other platforms, etc.
(And just to be clear, I'm not trolling -- I'm actually asking.)