Can I File For Financial Aid Before I Am Accepted At The Universities I Am Planning To Attend?

I am planning to return to college for Spring 2008, but I still have a few things I need to do (tests, references, etc.) before I wll have completed my application to the schools I’m considering.
Should I file my FAFSA as soon as possible..? Or do I need to wait until I have been accepted to a school?
If I need to wait until I’ve been accepted, then do I also need to wait until I’ve decided exactly which university I will attend? What if my decision will depend somewhat on how much financial aid I receive?