@OP, it all depends on the locality. Some places, nobody cares. Other places, the authorities will be all over you like a cheap suit. And as others have said, please do not attempt it without finding out first which it is where you are. Annoying the locals helps nobody.
Some states object mightily to transients sleeping over (even in an RV) in Interstate rest areas. Some take the more sensible approach that they'd prefer you not drive when exhausted, so sleep away. It is incumbent on YOU to know which it is. Usually there are signs saying "no overnight" but the mere absence of such signs should not be taken as an open invitation.
My daughter and son-in-law live in LA, and she tells me they have such a problem with otherwise homeless people living in RVs that there are city ordinances against it. She has told me that if we visit her in the RV, she can get a night-by-night permit to park the RV in front of their place, but not to attempt it without giving her enough notice to secure said permit.
On the other side of the coin, I've passed through Interstate rest areas that even had dump stations and special areas for RVs (but allow one-night only, it should be noted -- no hookups, they didn't want to make it TOO comfortable).
