These days, just about everyone accepts that we're running out of fossil fuels, and the airline industry isn't slacking in looking for alternatives. Electric aircraft and solar-powered planes have been successfully flown, but are a long way from commercial applications.
Biofuels are more promising. KLM flew a passenger jet this summer from the Netherlands to Paris on biofuel (regrettably gathered from meat precessing operations). EADS, the owner of the Airbus, has flown planes running on algae biofuels, and it working on a hypersonic jet that will fly at Mach 5 and be powered by biofuels made from seaweed.