I found out something interesting about beavers the other day...
I guess the dam building "reflex" is triggered by the sound of the water rushing. The beavers hear the sound, then follow it to plug the hole in their dam. Somebody did a study (can't remember who), but they found you could put a pipe in under/through a dam and keep the upstream part from flooding too much, as long as the intake and outfall were underwater. The beavers wouldn't plug the pipe, b/c they didn't hear the outflow.
I never knew that before. Might be some useful info if you have a drainage that you don't want to have to keep going back to clear out the beavers.
By the way, my boss uses small connibear traps to get the rabbits in his yard.