R.S.
Hi T.,
We always used to play a variation on hot potato: Buy enough small, inexpensive prizes for the number of children who will be attending the party (these could be in lieu of party favors). Put the "best" prize in the middle of a piece of newspaper and wrap it up. Then put another prize on top and wrap more newspaper around it. Keep doing this until you've made a large "ball" with many layers of prizes inside. Then, the kids play hot potato, and when the music stops whoever has the potato gets to unwrap a layer and get a prize before being "out."
We've also done face painting and had older siblings or their friends do some magic tricks (these might have been for kids older than 3, though). The hokey pokey and London Bridge are some other games you can do (old classics). Let me know if you'd like more specifics.
Best,
R.