If you are arriving at Rome FCO and want private transportation into Rome, I highly recommend Romecabs. We made a reservation via internet. It was 50 euros for 3 people rather an 40 for a cab. For us in our jetlagged half-addled state, it was worth 10 extra. The sharply dressed driver was waiting for us with our name on a placard just outside the customs area. We had a Mercedes air conditioned van. He parked the van and helped us with our luggage into the hotel lobby. We were very pleased.
Our hotel told us if we took a taxi the set price is 40 euros to central Rome -- but to settle the price at the airport as 40 total (up to 4 people) -- there is not supposed to be charge for luggage -- but many try to charge more. She said to refuse the ride if they wouldn't agree to 40 total.
That's good to know. On our last trip we stood in line a while to take one of the white taxis in the cab line outside arrivals, then we had an un-air conditioned ride into Rome. When we got to our hotel, he charged extra for the luggage, so we ended up paying about 50 Euros anyway!