Depends a lot on the type of valve; traditional compression washer with a packing washer around the spindle, or crane(TM)-type (also older), or more recent cartridge-type.
If this is a recent problem, and follows a repair to the washer or packing in an older type faucet, then it could be because of over-tightening of the packing washer or improper re-assembly. There has to be enough packing material so that the compression nut around the valve stem is back far enough from the valve seat to allow unscrewing of the valve handle -- if there isn't enough material, the stem will hit the compression nut instead of being able to open. Add more packing, and don't try to replace it with an o-ring. (I may have done this myself once, long ago - but am not a plumber). Over-tightening the compression nut may also make the spindle very hard to turn because of friction. You can address this by reducing its tightness, and/or coating the spindle with something called "plumber's grease", which should be available in small containers in the plumbing parts section of the local hardware store. In a pinch, you could try vaseline or mineral oil.
If it's a cartridge valve, I don't know.
Hope this helps.
Keith Simpson
February 2005