Books. At last count I have over two thousand. Some are displayed on shelves, others are in storage. The scary part is I've read many of them multiple times.
I also collect games, although not intentionally. It's just that when I find a deal, I pick it up, thinking I'll get to it eventually. I'm a bit behind on playing them though...
While we have a ton of DVDs/Blu-ray movies, I wouldn't say we collect them. It's just that we rarely go to the theater and often wait until they show up in the bargain bin before grabbing them. It's almost always cheaper than renting them, since we usually watch them a couple times at least (and if it's a kid's movie, they get watched several times).

oh, lots of stuff. Games - obviously(?). Trying to get the boxed copies and mainly buy on GOG and Steam when the price is great or if there is no other legal way to get a copy of the game.
At the moment I think I've got around 200 boxed PC games, something like 30 PS2 games, 10 PSX games, 130 Steam games, 8 GOG games.
Music (CD's, tapes, vinyls), movies (mainly DVD, but I've got 20 or so VHS's too. The cost of blueray players, discs and TV's capable of showing the difference isn't worth it).
I'm also trying to start a collection of synthesizers, but that isn't going very well at the moment.
I'm not collecting much for the sake of collecting, mostly it's stuff I'm interesting in using, watching, listening to that I like to keep after use.

I am a collector. And things, well things, they tend to accumulate.
On topic: I guess I collect games. Not anything else that I can think of though.

I also collect porn. (JK)
I used to collect old Star Wars peripherals. I have a collection of art from the 5th episode signed by the artist. I got to find that thing....

I collect furry cartoon animation and VHS tapes.

My major collections are {in no order}: Firearms, coins, knives, PC games {450+}, books{over 2,500},stamps, old fishing equipment, NRA caps, tactical & other military gear,laptop computer parts, fantasy & sci-fi art, comic books, trading cards{various subjects}, PC game maps & posters, and quite a bit of good old & new household dust. That's what happens when you are pushing 50 years of age! Oh. Wait! I forgot I quit keeping track of birthdays at 29.

I collect broken dreams.

Ever see Tommy Tricker the Stamp Traveller? It's like an Australian/Canadian love affair in philately.

I believe you.