Last year I was by chance on one of those Lufthansa planes that had Internet via satellite connectivity when flying back from the US over Europe. Despite the long round trip times, the overall experience was quite breathtaking. The only thing that can be done to reduce the long round trip delay times is not to use a satellite based but a ground based system. This is a bit difficult over the Atlantic but when flying over land, such a system is quite feasible.
While there are perhaps already existing solutions for ground based Internet solutions for planes, another alternative has been trialled recently: LTE to planes. According to this post and an even more detailed post here (sorry, both in German), Airbus, Alcatel-Lucent and Deutsche Telekom "flew" a trial in November 2011to see how well data could be exchanged between a plane and LTE base stations on the ground, separated around 100 km from each other. The post says that standard LTE equipment was used with antennas only slightly modified to direct the signal towards the the sky instead of to the ground. Speeds of 30 Mbit/s were reached in one direction and 17 Mbit/s in the other. The post is a bit ambiguous in which direction which speed was received but nevertheless that is quite impressive and shows that a cell should have more than enough capacity for the few planes that are its coverage area. At such a distance, the article says, 600 base stations would be required to cover Europe. That is just a handful per country.
But don't get your hopes up to see this in planes anytime soon, though, as there is not even yet a frequency band dedicated for this service.
P.S.: And I really wonder where the antenna was installed on the plane? :-)