I am a web hobbyist and don't derive a living out of web development, however, I think accessibility and usability are important.
Well, if you're building a site that MUST follow 508 compliance (dunno when that's getting upgraded in the States, here in NL we're getting a Web GuideLines update to WCAG2 this summer), then you'll need both the automated tools, as Mitt... Mittenseasagu... as the guy above said, to catch the easy stuff, and then go through it yourself... but then also consider hiring someone who checks these things for a living, because not passing 508 is surely grounds for a lawsuit or something, which your client will not like : )
If the site doesn't HAVE to be 508 compliant then I'd say automated testing, common sense and some self testing (you with a screen reader or magnifyer, on one of those crappy burnt-out lo-contrast monitors, with a dying jitterty mouse, and with no mouse, no JS, no images, text-only, etc) or better yet actual user testing if you happen to have anyone using AT or known web surfing issues/disabilities, all that should be enough for an average site meant for everyone.
508 is a very specific section of the law dealing with sites that either play active role in doling out Federal funds or information about Federal funds or themselves receive Federal funds. This pretty much means "government sites".
Heck, while you're at it, since you do actually care about accessibility, do some dirty user testing anyway. It'll point out the obvious (not to you) problems with layout, navigation, wording, etc with just a few people. Check out Steve Krug's (new) book: Rocket Surgery Made Easy. I'm going through it now myself. No point in saying, Hey, my site's accessible because it passed Cynthia or meets WCAG2... if people can't figure out how to use the darn thing because of poor wording or weird setups.