The idea that found its way to the top of my ideas list (it's a long list!) is a music composing app. Basically like Graffiti, except that instead of drawing stuff, you can compose little musical pieces and send them to your friends. You would do this by arranging notes on a small staff (the classic "like X except Y" pitch). Taking Graffiti as the inspiration, everyone would have a wall of composed musical pieces.
What I am concerned about a bit is the bandwidth. I wouldn't even be doing this if I didn't intend it to be popular. So assuming it is popular, perhaps people would be loading the composing/playback Flash application about 100k times per day. I did some calculations in my notebook (in a section titled "slimy biz talk corner") and this could mean a bandwidth cost of about $600/month. From my prior experience 100k page views per day for random people isn't necessarily greater than $600/month, so it might be that initially this makes no sense. However bandwidth is getting cheaper, and with Flash 9 there are things that would let me cut the size of the player/composer down A LOT so perhaps it would make sense in the future if not right away.
Oh yeah before settling (at least for now) on this idea, I spent two days basically pondering nonstop about which Facebook application to make. I wrote a long list of ideas that occurred to me, then ranked them based on how promising they seem. It's funny how many ideas for social apps you can find by reading a book containing playground games for children. For example there was a game where you must come up with something that you have done, but none of your friends have done. That would make a nice app as well. Anyway the point is that playground games books are a great resource =)