For the most part, it doesn't matter to me. I check out a lot of books from the library and don't really stop to think about paperback vs. hardcover.
When buying books, it depends. For something like Harry Potter, the last 4 books are so long that you really need hardcovers or they'll fall apart, plus since it's a set, I want it to look nice. But for most things it's nice to go with the cheaper paperback.
Looking at this thread...did I miss the announcement that our avatars have to be animals? I think I need to change mine to the cat.
I like to have hardbacks but generally actually read paperbacks. I have the opposite problem with things like the Harry Potter book - those books are so big that if I fall asleep reading and drop it on my face it's quite a painful wake-up call. Paperbacks are less hazardous. Also as others have noted they are easier for carrying around. I do a lot of reading on trips and I used to read on public transit when I used to ride public transit so a paperback is just easier.
At least twice I have bought a hardback when a much anticipated book came out but then failed to actually read it until the paperback came out.