Oh, my fiancee would love, err hate, this topic. She thinks I should throw everything broken away. Not me...I scavenge every last piece of stuff I can get out it. SOme of it ends up in the trash, but only after it's given me everything, and then some. Every once in awhile, I'll get enough stuff together and just start tossing parts together to see what I can build out of them.
But, I digress. I always keep the wires and stuff around for rigging and things like that. Honestly, I'm a huge fan of using wire versus thread for rigging up things, and it works well if you need some ropes on a ship or something like that. Plus, if it should be braided together...it's easy enough to do that to.
Another thing I have found is the thinnest welding wire, nonflux, that you can get. It works very well, but if you bend it around for too long, it will break.