A shut off valve in the basement won't budge. Brass on copper.

First try to loosen the packing nut and see if that helps. I hesitate to tell you put a big wrench on it because I have see stems twisted off. If you bee house aster off, shut it off at the curb box or well head.

Stuck open or stuck closed? Is this your main incoming water supply?

First, tell us why you are messing with this valve to begin with. If you are trying to shut off the valve so you can work on a fixture in the house you may be better off just shutting off the main water supply (if this isn't the main water supply) to fix the issue and bypass the trouble this valve could cause you...;)

Post back with more info...

Mark