I've had really good experiences flying with my cat(s). I moved two to England via Continental and they couldn't have been better. That was the first time they flew, so I was really nervous (plus, they're older). There were a lot of animals there and I was nervous they wouldn't make it onto the correct flight. You could tell the people at the reception center really cared about animals and they made me feel at ease. We flew into Gatwick and the people at the Animal Reception Centre were fine. One of the cats had peed, so they took out all of the bedding and put it in a plastic bag (which promptly got thrown away!). A couple of years later I flew them on a short Aer Arann flight from Cardiff to Dublin. Again, the airline employees were so funny with them. Obviously I left them prior to boarding and when I walked out on the tarmac to get on the plane there was an employee laying on the ground looking at one of the cats in the crate. It was hilarious! I was kind of hanging back watching and someone saw me asked if they were my cats. I said yes, and she told me how lush they were! Sadly, one of my cats died in Dublin (not from flying, because he was old), but when we moved to the US in June we flew one cat back with us. She was older (15!) and she flew like a champ! She's a nervous kitty in stressful conditions. This time it was Aer Lingus and they were brilliant as well.
Trust me, they do not want anything to happen to your pet and will do everything to ensure it gets there safely!