People ! ... I mean, body parts ( don't send the police here because FYI : they are well hidden) =p
Ok, seriously... now that I think about it, I believe there are three things I "collect".
1. Guitar picks, I'm fascinated by people who play the guitar, (specially if they are tall and cute =p ) so I used to ask for the guitar pick they were using. At this point, I don't even have to ask, if a friend or someone I know sees a special one (could be in a store, or "guarded" by another musician) they will buy it or get it for me ^^ Now I have tons and from almost everywhere !
2. Dreams !!! Since I was a child I always, always, always (if I had a dream that night, of course) get up and write everything I remember about my dream. Now I'm the happy owner of 4 notebooks full of nonsense, flying cats, rain drops, time machines, etc ... and still counting! ^^
3. Things for the head ^^ Everytime I have a party I buy a funny hat, a colorful wig or whatever I find "appropriate" for that ocassion and pfffff... My closet is full of that stuff now.
If I were rich?... I don't know... but if I take a quick guess, let's say I would collect big-amazing-powerful telescopes !