My daughter was about four years old when she attended her first slumber party. I feel now that she may have been to young because she returned home the next day with a broken collar bone from falling off the bed they were jumping on. I do not blame the parents because accidents do happen. My younger two boys have yet to attend a sleep over. Not so much because they may be to young but more because I do not know the parents who are throwing the parties. I do not allow my children to stay somewhere with people I do not know. Knowing someone to say Hi is not enough. My children's safety and well being is most important to me and that is why they can not just stay overnight with anyone!
First of all, I do not encourage staying overnight unless both sets of parents know each other well. As far as age, you know your child the best, so use your best parental judgment. I think minimum age would be 6 or 7 if your child is ready, you're close by and you know the family and neighborhood. Even though they're excited, for some kids, it's too uncomfortable once the lights are off.