Teams I talked to in California said they've entered competitive bots with under $500 in Vex parts, so I'm sure it can be done even if others are spending more. Rick is right about the reg fee, it has been $275, so at least while Vex was part of FTC you really couldn't do it for less than $700 - $800. But the Vex announcements in the Vex forum sound like the new events will be much cheaper, and if that's the case, then schools may be able to build and enter robots for $500-600 each. I hope so, that would help us start more teams and build more robots. Our school had to decide, and we're going with Vex next year since we know it's good and it's cheaper.
www.robotevents.com has lots of good information on it also, so you might want to check that out.
I wish FIRST would give more details about what exact parts are in the kit and what the prices will be. I also wish Vex would give more information about the virtual or online competition they announced. If it's free or cheap and has cool competitions, that could be really big too, but it's hard to tell with the little they mentioned about it.