I'm with randomman, I like to keep my stubs, if not for FF credit (should there be an issue), but also just for fun. I'm not a big fan of the thermal paper passes anyway. I think the first thermal boarding pass I got was on FL in 1998. They are way too flimsy and are just bound to be stuffed and crushed on the bottom of my backpack. The thermal paper was introduced at DFW a while ago, but I can remember traveling DFW-DEN-ASE in 2002 when I was a loyal CO flyer (before they decided to kill OnePass ) and being oddly thrilled that the Easy Check-ins spit out real card stock. A couple of times when I was flying CO, I had GA's refuse to reprint my boarding passes.

Another interesting issue for us *A-flying boarding pass junkies, is that AC FA's will sometimes stand at the door and collect boarding pass stubs. That struck me as odd.