Origami. I love Origami. It's the most relaxing hobby I ever had.
I listen to the Bombcast while I'm working out at the gym. Sometimes it's hard when I'm on the treadmill and they say something funny. I have to control my laughter so I don't fall off. If it doesn't finish during my workout I usually continue it the next time I'm walking the mall or something.
I usually try and play games that don't require too much thinking or text (makes it hard to concentrate to their voices when I'm reading). Burnout Paradise is very good for that, as is stuff like Geometry Wars and a couple of other things. I used to put in on my MP3 player and just listen to it while in bed, but I usually fell asleep in the middle of it (Brad's soothing voice is too much!).
As for what I do during Bombcast, I usually play a mindless FPS, or edit wikis. I am not blessed with the ability to multitask :-(
usually i browse the web, but lately ive been listening to them while i play, last 2 games i played were infamous and prototype, and outside the cut scenes, you dont have to pay much atention to the audio, and it helps while looking for blast shards or web of intrigue dudes :D