After a couple of dubious previous experiences at FCO, I got a recommendation on my most recent trip to try RomaShuttleAirport:
http://www.romashuttleairport.it
They were fantastic and made the transfer into Rome the best I've experienced. The cost was very reasonable (especially when traveling with a number of people, as I was, which makes the Leonardo Express unfeasible). Domenico, the owner, personally picked us up at the airport with a large van. I paid in cash, but they also accept credit cards, and I wouldn't hesitate to use them again and trust from for a reliable transfer into the city.