For international flights, KLM lets you check a bike for free, mainly useful if you want to bike in The Netherlands.
However, as of a few years ago, most airlines, even domestic ones, charge significant fees to bring a (non-folding) bike as luggage. A few summary web pages I found were a few years out of date, so I did some quick research (I’m idly considering taking my bike to New York in May to ride the Five Borough Bike Tour):
Typical* domestic fees, each way, as of January 2012:
* The fine print: fees sometimes vary based on size and weight— I estimated typical fees assuming the boxed bike weighed less than 50 lbs but was well over 62 dimensional inches (length + width + height: 80-100 dimensional inches is more common for the boxes I’ve seen). Also, some small regional airplanes (sometimes run as codeshares with larger airlines) may not allow bicycles at all. Call to be sure.