Most amateur and enthusiasts' digital SLRs use the APS-C format, and full-frame sensors are generally reserved for much more expensive professional models. The latest advances in sensors mean that the quality of images from APS-C format cameras can be very high indeed, though these same advances also benefit full-frame sensors, so the gap in quality is still there.
This diagram shows the relative size of APS-C sensors and full-frame sensors. It also illustrates why you have to apply a 'crop factor' or 'focal factor' (1.5x or 1.6x, depending on the exact size of the sensor) when working out focal lengths with APS-C format digital SLRs. For any given lens, they capture a smaller angle of view than a full-frame sensor, which gives the effect of shooting with a longer focal length.
