Here's the "
Airline Baggage Regulation for Bikes" page:
http://www.ibike.org/encouragement/travel/bagregs.htm
If you scroll down, you'll see a chart of a large collection of airlines and what they charge for bicycles.
We're flying Qantas next week, and if you scroll right down near the bottom of the page, you'll see that bicycles fly for free.
You do, however, have to check with the actual airline before making your decision who you will fly with. Airlines change their prices and policies frequently. It is good to check even after you've booked, shortly before you fly, to make sure that nothing has changed again in the weeks leading up to your flight.