Well, the answer is more complicated than you're going to want to hear. I just used the tool online at fafsa.ed.gov, and the answer I got was that for the 2015-2016 school year the deadline is June 1, 2015 by midnight, Central Time (for some students!)
That's actually the state deadline (for New Jersey), and for Tuition Aid Grant recipients. There's also a federal deadline, and your college may have one too!
The bottom line is that the FAFSA application requires the same kind of information that you (or your parents) use to file income tax returns. That information is typically close at hand now, so why not apply now and get it done?
If you're not from New Jersey, or want to see more detailed information, click here and check out the deadlines applicable to you!