Burchey, call me crazy, but I generally try not to cut my rope or webbing when climbing. I'm funny that way.
Sorry, couldn't resist. Seriously, though, can you expand on that? I have only a limited amount of technical roped experience, but I'm trying to picture a situation where I'd need to do that.
Hey Bulldog! You're crazy!
Seriously though, there are a few situations where cutting webbing/rope would be necessary. I recently revamped my umbilical system - used my knife to cut the webbing then, and I noticed how easily it sliced through it. On the mountain, there are rare occasions on maybe a multipitch climb where rope could get caught, etc. You may need to get loose somehow.
On Rainier, we ran across a very dangerous spot beneath seracs, where I was ready to cut myself off the rope ( tail-gunner ) if they came down so I could escape the falling ice backwards while the other guys continued forward to escape it. We were crossing a chute, basically, and if one guy's on the other side, and I'm just starting the chute, ice comes down and drags us all down the mountain even if it misses falling on us directly.
EDIT: This is the spot, we were crossing where the river of ice went
River of Ice 
