No Overnight Parking at Interstate Rest Areas

Wow, I didn't expect such a lot of answers! I realize I wasn't entirely clear in my original post-- by "staying" in rest areas, I didn't mean "camping". No slides, no chairs, no anything other than parking, walking the dog, maybe having lunch or a late dinner, and then sleeping. Sometimes it's just a nap, sometimes it's been overnight. Even if it says "no overnight parking," if we are tired enough and it's dark and late in the evening, I figure it's better safe than sorry. Once we did that in Ohio, and it was only later than I discovered that there's no "overnighting" on I-70 rest stops. I-80/90 (the Ohio Turnpike) doesn't have a problem with it, so I didn't know. But no one bothered us anyway. Which was a good thing, because we were exhausted and really needed to stop.

It seems that no one really has had any experience being told "you have to leave now, you can't park here overnight." So I guess that answers my question! Thanks to all who weighed in!