I collect various types. Some first editions, some special editions by small press houses, autographed editions, et cetera. I have a UK edition of The Last Hero by Terry Pratchett. It's autographed, too.
Right now my main focus is on collecting various autographed editions of Tim Powers' books. I have some stuff I'm ditching though, like my copy of Dune: The Butlerian Jihad which is autographed by both authors.