I haven't trapped any beaver for the last couple winters, but before that I used to catch a handful each season.
My wife actually thought it was kind of funny when people would call and ask for me, and she could tell them "He's out in the garage messing around with a beaver" or "He's busy scraping the nasty stuff off of a beaver" (she was referring to the skinning and fleshing process). After I fleshed them I had to tack them out on a sheet of plywood or a metal hoop to dry, so she also thought it was fun to tell people I went out to the garage to stretch beavers!
On a side note- BBQ sandwiches with beaver meat (or even muskrat, for that matter) ain't bad at all! Actually, if I substituted the beaver for the beef, and didn't tell you, you'd never even notice it...
Man I loved trapping! I basically quit when I started falconry, since they both happen at the same time of year and the birds take up all my time now...