I admit it. The only thing I collect is paper. Masses and masses of paper that cover my desk, which unfortunately is also my dining room table. That may be why I'm always up for eating in front of the television.
I admire people who have the foresight to hang on to trinkets. I had some pretty cool stuff when I was younger, stuff that would be worth money now. Star Wars collectibles and Barbies. And I tried collecting Christmas ornaments the first few years of my marriage. Each holiday season I'd find something with the year on it. 1990 - 1994 was the limit of my attention span. I've occasionally purchase a dated ornament since, but it's too depressing to note all the gaps in the timeline.
Giving your character a collection can reveal oodles of information about their likes and dislike, their personal habits, and that spark that drives them. In my case, my Christmas ornaments say I'm scattered. Or maybe I'm not attached to material things. Yeah. That sounds better.
A history buff could collect stamps. So could a greedy kid who heard there was money in postage. An invalid could live vicariously through a postcard collection and arrange them on a map of the world, but an insatiably nosy person might file them by message type: lovers, parents, and friends.
Collections can also tell the reader something about a third party. When your sleuth interviews a witness who is surrounded by stuffed cats, does he absently stroke the black one and reminisce about his favorite childhood kitty? Or does he immediately dismiss the hobby as an obsession or a waste of money.
The next time you describe a character's home, throw in some unique passion - coffee can lids or porcelain ostriches, and then let the reader paint the character sketch from his own imagination.