Is there any airline that has internet available for passengers on flights? Is there free internet available on flights?

Currently I think only American Airlines offers in-flight internet access on select 767 transcon routes in the U.S.A. The fee is $12.95.

For a few years several airlines (SK, LH, SQ) offered in-flight internet access with equipment and satellite service from Boeing Connexion, but that service has been discontinued. The fee for that service was ~ $29.95 for the flight.