According to The Seattle Times:
In recent years, transporting pets on commercial flights has grown more complicated — and more expensive. All major carriers have significantly raised the fees they charge for bringing pets onboard, matching, or in some cases surpassing, the $100 surcharge each way they typically charge for children flying alone.
Airfares vary widely depending on how your pet travels – in a carrier under your seat, as checked baggage or as cargo – from around $100 one way to $250.
The safety of pet air travel has become a significant issue in recent years. As the number of traveling companion animals has increased, so have incidents of pets being hurt, lost, or dying en route.
According to the Department of Transportation, in 2010, 39 animals died aboard U.S. flights; 13 pets were injured and 5 were lost.
Air carriers impose limits on pet travel, including maximum and minimum temperatures at which animals can be flown, as well as restrictions on certain breeds like flat-faced pets prone to breathing difficulties. For example, Delta no longer flies Bulldogs after several fatalities occurred during travel last year.
Believe it or not, there's an airline exclusively for companion animal travel called Pet Airways. This carrier offers pet-only flights to around a dozen major U.S. cities. Pets fly in the cabin in individual crates, and a flight attendant checks on them frequently. Fares range from $99 to $249 one way.