Here in New Zealand you'd tend to get their bank account number and send them a (free) direct deposit through your bank's Internet banking service. Until very recently that was also the main payment method for our eBay auction site equivalent TradeMe (they've now started a sort of PayPal clone called Ping so that they can skim a little extra from each auction).
But I've heard people can potentially withdraw money from your account if they have your account number in the US?