I have many...mostly AF and USN from my time in and with the service (ongoing). Also, many stickers covering the kegenator I had in my ACMI facility to facilitate debriefs; the tap handle is a 30mm round from an A-10.
When I was younger, I did. Usually sports teams, racing-related, or random patches that were available. My dad knew some cops and military guys, and they were always willing to give some extra or old, worn patches to a little kid! I have some old Chicago PD patches, which I like to imagine were worn by some cop who beat the **** out of hippies in 68, but now I'm thread-jacking...
I have some from a couple areas where I was stationed. I also have an old USA made TAD OD green hoody jacket that has velcro that I change out patches from time to time.