Most people eat the gar, buffalo, drum, and other fish that they take. Some are lucky enough to shoot really tasty things like rays and talapia. The bighead and silver carp are supposed to be very good also.
I know quite a few people who even eat the common carp that they shoot. I've brined and smoked carp in the past and it's really quite good.
The carp in the area I now live in are contaminated with PCB's and have a '1 meal per month' advisory. So... I don't eat carp from my area.
Sometimes bank fishermen want them and I'll give them away but I worry that I'm poisoning someone. [:'(]
Usually I just take them home, toss them in the freezer and then throw them away on garbage day.
Remember, common carp are detrimental non-native fish. Every one removed from our waters is a step in the right direction.