I just noticed my sump pump is running off and on constantly.  I hear
water draining but I see no water anywhere.  The area around the pump
is dry.  I have no idea where the water is coming from.  We have very
little snow on the ground.  Not much rain.  This has never happened
before. Where could so much water be coming from?

Feel the pump itself - if you can feel the motor running but no water
is moving, this could mean there's a clog in the pump screen or the
drainpipe. Unplug the pump to check both of these.
http://www.ehow.com/how_16651_troubleshoot-sump-pump.html

I had the same exact problem. The Check Valve is the problem. I had a
small amount of water. It was enough to kick off the pump. The pump
would drain the bin and then turn off. When it turned off, the water
would run back down the PVC pipe and back into the bin and then kick
off the pump again.
There will probably be a check valve somewhere in the hose or PVC pipe
that your sump pump outputs the water to. It will be rubber with hose
clamps on it. The valve only opens one way (output). When the pump
stops, it will close and hold any water in the pipe from running back
down into the bin for the pump to go off again.
These valves are under $20 and can be found at any Home Depot. It
doesn't require more then a flat head screw driver to replace.
Good Luck!