When the rear wheel is spinning, and you try to hold the cranks stationary does the rear wheel still try to drive the chain?
Does the chain get all tangled up as the rear wheel spins and the cranks are still?
From the looks of it you have a bad freehub body on the rear hub. You need to get a replacement 8/9/10 speed freehub body
from a LBS or online.
Unless you have a dork disk that I can't see, that's rubbing on the cassette, then it looks like the cassette body needs replacement. The freehub is simply not freewheeling the way it should, freely. Oldskoolwrench's advice is spot on except for the chain tangling part. If you don't get it fixed, though, you will get the chain tangling before summer's over.
Unless you're already handy with cone wrenches, I suggest taking to wheel to a shop where they'll dismantle the hub, find a replacement cassette body, and put it all back together.