With an account number and your real address they can make money transfers direct from your account, by pretending to be a business you've made a purchase from.
In the UK there's no charge for using cheques, many people over 60 use nothing but cheques ;-) When I've mailed cash before I've sent it 'internation signed-for' - it's cheap, and provides feedback on weather the recipient actually got the envelope (and probably puts off some would-be thieves). Don't know if the US has an equivalent though!
