Is crouching in Quake Live useful?
Solution 1:
IMHO, no.
Let me explain: crouching allow you to reduce your exposed surface, making you a smaller target. It could be useful, but crouching has a downside: it impedes your mobility by reducing your speed.
Since most of the weapons allow somebody to one-shot or two-shot you, good speed and unpredictable movements are your greatest way to survive. That's why most of the time, crouching is the easiest way to die.
Solution 2:
yes it is. Crouching reduces the amount of surface exposed to a possible enemy hit, while it is pretty much useless to use while walking it is usually used in midair, especially if you're moving in an area where you are an easy target. It is not a big deal tho, sometime people may miss you because you crouched, but good players know how to shoot
Solution 3:
Crouching in an unexpected moment can save your life. One example is a shotgun infight - a crouch in the right second can negate a otherwise full hit. Same goes for rail gun fights at medium distance.
And yes, for gauntlet as well.