I've left my phonecell once on a taxi in Rome after a trip FCO-downtown. When I realized it was half an hour later. I called my number from the hotel, the taxi driver answered to my phone and came to the hotel to give back the phone. I insisted to pay something for that, he didn't accept anything!

Apart from that, FCO is one of the worst place for taxi-scam. You see taxi drivers, limo drivers, not authorized drivers, others, all asking different fares. Their preferred target are Japanese tourists. Always choose a regular one and check that they apply the fixed flat fare to te center of the town.