1. Can be used to apply for and verify an account with Bitstamp, Kraken and other exchanges. (they then transact stolen coins and funds there which, if later traced, can and will wreak havoc on the real ID owner's life, financially, personally and even professionally).
2. If the ID provided is comprehensive enough (passport, SSN, proof of address etc) they can be used to apply for sensitive accounts online (bank accounts, credit or debit or prepaid visa/mastercards) which in turn are used to receive stolen or scammed funds. The funds are then used to buy coins or to perpetrate illegal transactions.
3. ID can be cloned and used by impostors who pose as the real ID holder/owner. Someone's credit score will suffer. Not the scammer's, for sure.
4. Scammers can use the ID to initiate transactions here and offer identity verification as a form of escrow. Guess who suffers the consequences when the deal turns sour.
etc etc