You can use it on T-Mobile or AT&T in the US, but not Verizon, Sprint, or any other CDMA carrier.
Plus, you will only get 3G on AT&T and only in areas that don't use the 850 spectrum.
If you like the European Galaxy S better than any of the US ones, the Bell Vibrant in Canada works on AT&T's spectrum and is the same as the European model.