We flew from Sri Lanka to France with two dogs and a cat. As far as I am aware, animals can only travel in the cabin on certain domestic flights within the US and must be in the hold on long distance flights. But as Alan says, you need to check with the airline.
We chose Emirates as they have an excellent record for handling animals, and indeed the captain himself came to my seat in Dubai to reassure me that he had checked on the cat at that all was well.
I read a vast amount and consulted a great number of experts before we shipped our pets and the advice was most strongly - do not sedate animals before travel. It can cause complications in their breathing and can make them much more distressed if the effects wear off before the end of the journey.
We fed ours in the morning before a night flight (so 12 hours without food before flying) and made sure there was a water bottle attached to the front of the cage with a bowl beneath it so there was always water available throughout the journey. We also put a handful of dry food in a sachet taped to the top of the cage for the transit in Dubai, but this wasn't used.
Clearly, its not fun for animals to travel, especially noisy, excitable ones. But once they arrive and are reunited with you, its like nothing has happened. I was amazed when we went to collect our dogs; as soon as they were out of the cages everything was back to normal.