Just to add to the airline crowd, I shipped the NajaHound from Denmark, a 16 hour flight, via Lufthansa with no adverse happenings.
Generally speaking, you cannot transport a pet in the passenger area of a commercial aircraft unless it is in a pet carrier that must fit under the seat. The only exception is a service animal.
Checkout this for more info —> http://www.airlines.org/customerservice/passengers/Air+Travel+for+Your+Pet.htm