I use a Bore Snake for my shotgun--man, does it make things a heck of lot easier. Like the others said, it's best to use after each outing. Otherwise you'll be running grime back through the bore again when you have to do a second or third pull.

I do a lot more shooting with my rifles and pistols, and I use the Dewey nylon-coated rod that skeeter 7mm mentioned. It's a lot easier to give the bore a good, sound scrubbing with a traditional brush.