I read a story once about Larry Carlton breaking his high 'E' string during a solo. He then proceeded to take out a pair of nail clippers and cut the 'B' and 'G' strings, and played the rest of the solo on just the bottom three strings.

Breaking a string is not a big deal, easy enough to continue until the end of the song, unless you have a floating tremolo system as Herb mentioned, then you are pretty much screwed. I haven't used a guitar with a whammy bar for probably 20 years, but when I did I had the springs tightened up so that it could only bend down, that way the guitar would stay in tune if I broke a string.