I wouldn't call myself a DVD 'collector', per se. But I do like the feeling of buying a new one and putting it on my shelf with the others. Many of them I've only seen once (and a few not at all), but seeing all of my DVDs in one place kinda makes me feel all good about myself and the good films that I've watched. As far as other traditional 'collections' go, I'm not very good at them. I used to collect Beanie Babies when I was about 8-years-old and they were an OMG MASSIVE CULTURAL TOUCHSTONE, but once those became less popular, my collecting instincts died along with it. It's good in a way because I don't have hoardes of stuff that I don't need, I guess... but I never really get invested in anything because I don't have that innate desire to collect 'em all. Even with Pokemon, I've never had the desire to catch all of the ones in the game. It's just not in my nature.
I collect trinkets from friends that I can keep with me whilst moving around the country for when I want to remember them. Generally stuff like beaded bracelets, necklaces, plectrums, coins, things like that. It's a little odd I know but it's always nice to have something to remind you of home when you're lonely and away from everyone. I also used to collect cuddly toys when I was a lot younger but grew out of that pretty quickly haha. So soft and squishy ahh ;;
Free stuff from hotels (directories, business cards, pens, notepads, laundry bags, etc. I have a Quality Inn directory that dates back to 1979.)
Anime DVD's and manga
Automobile brochures (my oldest dates to 1978)
Business cards in general.
And for something in non-digital form, fanart of anime girls (Leaf, Pretty Cure etc.)