The short answer to your question is "typically, yes, you do have to be out of the house you are selling on the day of closing."  The more complicated answer is "it depends on the contract between you and the buyer(s)."  Most real estate contracts I've seen --at least the "form" contracts used by the local real estate board or association-- contain a clause that allows the parties to agree to a possession date.  They also typically provide the ability for the parties to set a per day penalty if the seller does not vacate the premises on the possession date agreed to. 

If the parties did not provide for a date of possession in the contract, the buyer would probably have to take the seller to court to enforce the buyer's right to possession -- and win.