After numerous moves in my early 20's and letting random roommates borrow things to never see them again my DVD collection died and I haven't bothered to bring it back.
I do like to collect video games and consoles. I still have all my old ones and add to their collection if I see a good deal.
I like to collect Books but I have no problem loaning them out if I think they're a great book and someone wants to read it, I just never expect to get it back.
I did recently start collecting shot glasses from places I travel. They're nice little mementos of good times, I've got one from the House on the Rock, Mackinaw Island, Boston, Kansas City and like 4 others from Missouri.
I have to say the Austin one is my favorite though, that one has the best story.