Usually, when I like a book that is in a series, I'll go back and read the series from the beginning, and then try to find more by that author.
I re-read less often, though. The exception has been LOTR, which I've read several times, just because I love the characters and the setting, and the movies, too.
When I come across a new author I like, I'll try to read as much of their work as possible - my wife got me started reading Stephanie Myers with the
Twilight series, but I went on to
The Host, and she didn't. (spoiler: The Host is better!)
I just started reading
A Wild Sheep Chase by Murakami, and I really like it... so I'll read more of his work, even though I don't think he writes in series... I could be wrong.