A taxi to the centre of Rome costs €40 for up to 4 people, including luggage. The fare is set by law and the taxi drivers adhere to it (since they don't want to lose their right to operate from the airport). I've been stranded in central Rome after missing the bus back to the airport, along with an American traveller. We took a cab from the station taxi rank and he charged us exactly the correct fare for the journey, as displayed on the signs at the airport.
Cotral operate a bus service from the airport to Rome Tiburtina railway station. A ticket will cost you €4.50 if you buy it at the airport (in a newsagents shop, for example) or €7.00 if you buy it on the bus. It's the cheapest service, but the least frequent.
Buses leave the airport at these times:
01.15 - 2.15 - 3.30 - 5.00 - 10.55 - 12.00 - 15.30 - 19.00
Buses leave Tiburtina station at these times:
00.30 - 1.15 - 2.30 - 03.45 - 09.45 - 10.30 - 12.35 - 17.30
Sit Bus Shuttle operate frequent services to Via Marsala from the airport. Timetable here:
http://www.sitbusshut...orari_bus_shuttle.pdf
The fare is €8 single or €15return. Tickets can be purchased on the bus.
L'Autonoleggio Tirreno operate frequent coaches to Ostiense Station, with a €6 single fare. To view the timetable, go here:
http://www.autonoleggiotirreno.it/
Then click on the Autolinea Diretta box.
Chris