You can apply for scholarships at any time. If you are talking about the FAFSA you cannot apply for it before the application is ready for you.
So if you are entering you senior year now you can start applying to universities in the fall of 2009, the winter of 2009, and (sometimes) early spring of 2010. It's important to find out the application deadlines for all the universities you are interested in and mark them on your calendar. You should also find out if you need to write any essays or have any letters of recommendations written. If you do, start on the essay early and work on it when you have spare time and ask your teachers early so they have plenty of time to get it all done.
But you cannot apply for the FAFSA until January 1st of 2010 because you will need the 2010-2011 FAFSA application. If you fill out an earlier application you will just cause a lot of headache for yourself and the staff at your university's financial aid office.
In order to fill out the FAFSA you need your (if you have a job) and your parents' tax information so make sure you get your taxes done early!
it is also important to find out each state's FAFSA deadline and make sure you complete it by then. If you don't you may not get as much aid as you could have had you been on time.