When I was younger, I collected all sorts of rocks and stones (I still do sometimes, if I see one that I like the shape of). My parents didn't know what to do with them... I moved on to giant branches that had fallen from the trees on our street, which were moved to the garage when my parents got tired of seeing the things in the yard. As I got older I stopped collecting as much because I just didn't have anywhere to put it...
My dad tried to get me interested in stamp and coin collecting, but they were boring to me. Why collect little pieces of paper and metal? They're all the same! I would much rather have a collection of unique rocks that I found in my yard than some old coins that I had bought from some other collector or something.
At one point I tried to collect soda bottles and cans but the parents didn't like that either....
Right now the only things I collect are anime figures and Transformers toys. They're not as "useless" as the other things, according to my parents, so they let me keep them. Once I get older and get an apartment or a house I'm sure it will be filled with all sorts of collections!
I also have a small collection (well, by my standards) of pins and buttons that I used to keep on my messenger bag. I got too many, though, and I ended up taking them all off and getting a new bag
They're now sitting in a pile on my bookshelf...
I also collect Magic: The Gathering cards, though I took a break for a few years. I recently rediscovered my love of the game, though, and have started collecting again.
If this counts, I also collect mounts and pets in World of Warcraft. I'll grab as many as I can get my hands on... if anyone else plays, I'd be glad to tell more about my collection