We see a LOT of campers who rig up some type of fence. Although technically I believe it's against almost all campground rules, as I've yet to encounter one that didn't specifically say pets were to be restrained on a leash no longer than six feet. But obviously it's one of those things many campgrounds overlook.
Some private campgrounds have dog runs. We've stayed at places where the dog run was fantastic, and places where there was no way on earth our dogs would be allowed to step foot in the run.
If you're near fairly populated areas, it's usually not too difficult to find a municipal dog park. I'm not a fan of public dog parks, but if you can hit them on weekdays when most people are at work you can usually avoid big crowds and too many rowdy dogs.