I think maybe around age seven. If you do it too soon, they may get homesick. Then, the next sleepover when they would have been ready for will be filled with anxiety. It's best to wait a little and be on the safe side.
--------------------------------------------------------------
Old Glory
I remember going to slumber parties when I was ten and being ok at my friends house. Earlier than that though and I was only allowed to stay at family homes. I always think it is a good idea though for the parents to meet before anyone does any staying over and only go through with it if you are totally ok with it.