If there really is no way you could afford it without aid, then you'll get aid. Rice is very good about need-based aid. Unless you mean your parents will refuse to pay, in which case I don't know what to tell you...
I applied ED and got need-based... it wasn't amazing, but it was manageable. I mean, they aren't going to throw money at you, but they make sure your parents don't have to live on cans of beans to support you through college. Every once in awhile they can afford bread and meat! lol

My aid package is better this year than it was last year, so I'm pleased.
Rice raised their no-loan cut-off this year (for 2009 matriculants on) to $80k, and a few other things. Look at their Financial Aid site for info on that. And if you have any concerns, I wouldn't hesistate to call the FinAid office and ask for advice, etc.