When my wife had some minor surgery (not fully anesthetized), there was a nurse present who counted all of the sponges, etc. that were used, then made sure there were that many on the tray at the end. They didn't match up, and it turned out that the surgeon had dropped one off of the table.

The article mentions that counting is standard procedure, so hopefully this is how it works everywhere. It definitely seems like having someone who isn't the surgeon doing the counting would be the way to go. The surgeon is already very focused and it's easier to say "I'm sure I didn't leave anything" when someone else isn't telling you otherwise.