You don't need funding, but getting money lets you take advantage of the irrational exuberance of the VCs or the FREE MONEY that the Facebook grant fund is offering.
I got this advice from someone when I was considering applying to AppFactory.
"I would say multiply the number of team members by the time period you're asking to be funded over, by a very high valuation of your team members' time ($75/hour, say), and add some server costs."
Didn't end up applying to AppFactory, but maybe I should write that application now that there is the FB grant fund with even better terms (free money).
For anyone curious, one of the facebook platform ideas was to make a Sim City type game for the facebook platform where your city got bigger and better as more people viewed it or you invited them to make their own neighboring cities.
Kind of like this French site, where you build a city by having people go to your web site. http://rms.miniville.fr
Do you really need funding, or do you need financial motivation to do the work?
I would suggest if you really do need some funding for some specific costs, you should take as little as possible :)