If my characters stop speaking to me, then it usually means that I've tried to force them into something they didn't want to do. Sometimes I've taken them down the wrong path and have to backtrack and see where they deserted me. Other times, they just aren't ready to deal with whatever it is I'm trying to write (usually for emotional/psychological reasons).
I don't plot, though, so sometimes I can just move to another place in the story and leave the challenging scene unfinished until they're ready. I don't write linearly, either, and sometimes what needs to be done is to write an earlier scene to prepare the character for the scene in which I am blocked.
If the words stop flowing altogether, I also leave the computer to take a shower, nap, or walk. Any of those things will usually bring the characters out to tell me what I need to do or fix. I never used to have writer's block for long periods of time, although now when I go weeks without writing, it's usually due to handling business things like events, taxes, etc., rather than actual writer's block.