Re: 10D and EF-S 10-22mm
No it won't go on the 10D. At least not without modification of the lens. It uses the new EF-S mount, which is an EF lens with a protrusion to prevent it from mounting on regular (read EOS film cameras) bodies, because of mirror travel or some such thing, the mirror could hit the lens on a film body, damaging one or both. (Or at least I think that is what will happen.)
Some folks over at dpreview.com have found that if you remove the protrusion it will fit and work on the D30, D60 and 10D bodies. There are hacks on the dpreview forums instructing how to remove the protrusion and use it on older D series bodies.