You could be fined, towed, or even both.Added: It is a local or state statute or ordnance. In some jurisdictions the monetary fine is hundreds of dollars.
It depends on when and where you park and for how long. You obviously don't want to park in handicap spaces or valet spaces without permits, and you won't want to park there overnight.
The default answer is the car that is moving is at fault unless the moving car has the right of way. However parking lots are messy and there will be no police reports unless the damage is over a...