Wouldn't go overboard at this age, but pass the parcel seems to turn up at most parties at this age. The best version I've seen is a tumbletots one where you pass a beanbag round the group, and when the music stops each go the "winner" gets a small prize. There was no large prize for the ultimate winner, but everyone got a go and won something small (in that case it was actually a medallion with "I'm a winner" on it!). Much quicker, no risk of getting the number of layers wrong, or suffering if a child tears off too many layers.
Statues and Pin the tail are also favourites. Best to stick to well known games as trying to explain the rules is a nightmare - I'm sure those 3 work so well because all the parents instantly know what the rules are and persuade their children to confirm...