At the particular park I mentioned, there are signs telling people to be quiet, not to bring pets, and to walk, not run or ride bikes. But, apart from signs, there's not much.
Not everywhere does want visitors though. At least not as much. Some places are deliberately managed not to encourage lots of visitors. In this regard, wildlife refuges out west come to mind. There are huge spaces kept undeveloped with no infrastructure so that you really have to make an effort to get in and out. You can't just drive up or walk a mile and be in.