Roger, the really grown-up ones have all that you'd expect of a decent SLR (the Nikon and Canon versions of the Kodak digi-body for example).
Moving down the scale to the compacts, many of the better ones (Canon, Olympus, Sony) have some degree of manual over-ride - in that you can adjust the exposure a couple of stops either way. But, if you want to retain total control, you're stuck with buying a very expensive bit of kit.