No, but I have been asked for my state ID each time I've done it (unless I'm already in their computer like Saturday Matinee), along with my address, phone number and signature. It's a hassle, but I can see why they do so.
Like a few months ago when I traded in probably 13-14 GC, PS2 and GBA games to the Saturday Matinee to get an Xbox (the credit came pretty close, $151.50, I only had to pay $42.55 for the system in cash), I can fully understand why they would want all of that information from me. If I were working there, I might be a bit on-guard when someone trades in a who lot of material.
Fingerprinting might be going a little too far, though, and I can't imagine that this would help anyone who has had their property stolen recently get their stuff back by fingerprinting. If they decide to fingerprint customers in a lot more stores, perhaps they can mask this by promotion.
What I mean is, if you're a frequent trader, make them put a fingerprint on a card, and when they present this store ID card, they could get 5% or so extra credit or 5% off their purchase. I think providing incentive is a good way not to scare off potential traders (that do not possess stolen property) that may think that their information will be sold or something like that.