In short, No.

Canon APS-C or cropped sensor bodies have more distance between the mount and the mirror because the mirror is smaller in the APS-C body. A few wider angle EF-S lenses take advantage of this travel and extend components further back into the body at certain zoom and focus positions than a standard EF lens. So, if you try to put an EF-S lens on a full-frame body, the back of your lens might hit the mirror at certain focal length and focus distance settings. However, you can put an EF lens on an APS-C body without problem (well, at least no physical mounting problems). So, at least you can upgrade your lenses knowing that they will always be backward-compatible with your other camera(s).

In review:

EF-S Lens and APS-C -> YES!
EF-S and full frame -> NO
EF and APS-C -> YES!
EF and full frame -> YES!