The way I understand it, a SIM card removed from any GSM phone will work in any phone from the same provider, or just any unlocked phone. If you stole a SIM card, AT&T would probably be able to get the serial number of the phone you used it in. Whether or not the SN could lead them to you depends on how you obtained the phone. If they really want to get you, they might be able get a warrant to tap your calls to try and identify you, or they might try to get your postion using GPS or just the nearby cell towers.
But half this stuff I am not 100% sure on, so please correct me if I am wrong.