I don't go to many parties. But when I have get-togethers with friends, pizza and cake obviously are favourites. I like to drink soda too, whenever I get the chance, as it's rare here. One friend's mother made honey mead for his birthday and that was pretty fun.
It depends on who I'm with.

If there are a lot of writers at a party (this is speculation, as I've only been to a few birthday parties that I can remember to date), I would imagine it would be great fun to do a collaborative story, where you either have a notebook and write down a paragraph or so, then pass it to the next person. (Or just speak your part out loud, and then the next person starts telling the next part of the story, etc.)
With my friend Anselm, the parties I've gone to with him (either his birthdays or a mutual friend's birthday), we like to play roleplaying games where we pretend to be movie or book characters; explore the woods, swordfight, go through obstacle courses, etc. Capture the Flag is a popular game as well.
In my world of Solarii, there are different cultures and races, so it's hard to pinpoint just one sort of party food. The Light Elves of Daerdan would have a lot of fruit/berries, a lot of vegetables, and a lot of breads, I believe, for example.
I need to think about celebratory events in my respective cultures... thanks for bringing up the idea!