Katie,
You can totally have a fun and managable birthday party for a 3 year old. If you keep the numbers down to 5 or less kids, they won't get bored waiting for their turn at the games or choose activities or games where everyone participates at once.
My suggestion would be to plan for an 1 hour or 1 hour and a half birthday party for that age group. Pick a theme first since that will help you decide which games to play. Break the party down into a game (15 - 20 min.), a craft (15 to 20 min), cake eating (10 - 15 min.), and maybe freeze dance as a fun activity(15 min.). If you have the party at your house, let the kids just play and explore for a few minutes. Definitely ask the parents to stay at the party to help out and mingle. (I've met some of my best Mom friends standing around at toddler birthday parties.) Have some adult snacks on hand and don't be afraid to ask the parents standing around to help run an activity.
My last suggestion would be to not open presents at the party for that age group. First, it's boring for everyone who is not the birthday boy or girl. Second, the other toddlers might start crying and getting jealous of the cool gifts they can't have. And finally, this happened once or twice with my kids, toddlers say the darndest things and they may say something inappropriate or rude about the gift and as the Mom you are mortified.
As a shameless plug, I was just on NBC TV Chicago and WGN TV talking about how you can throw a fun, unique kids birthday party at home for under $200. If you want to watch the video clips for more ideas, you can see them here - http://www.chocolatecakeclub.com/kibipath.html.
I hope that helped. Feel free to email me at ____@____.com if you want more info on age appropriate games. Good luck!
S. Kirchner
www.ChocolateCakeClub.com
www.ChocolateCakeMoments.com - Simple, Creative & Memorable Ideas for Family Fun!