G lenses work on almost every autofocus Nikon. I have personal experience with the F4, on which G lenses work, but you are limited to P and S mode. VR doesn't work, but AF-S does even though the F4 predates AF-S technology by quite a while!
I'm pretty sure APS-C lenses can't be used on anything other than the Proneas, but DX lenses can indeed be used on 35mm bodies as well as FX. The amount of falloff varies from lens to lens. It also varies based on aperture, focal length, and focus setting. A lot of Thom Hogan's reviews of DX zooms will tell you what focal lengths are usable without vignetting: http://www.bythom.com
Edit: Also look at Kav's brilliant post above! We posted at the same time but his is much more useful.