Maglev trains are trains that levitate about 10 mm off the tracks using repulsive electromagnets on both the tracks and the train itself. This levitation greatly reduces friction, potentially allowing the train to move faster and consume less power than it would otherwise. There are no regularly used maglev trains, though test tracks have been built in Germany, the USA, and Japan; including the MLX01, located in Japan, which is the fastest train ever built at 550km/h (344 mph). There are plans for a maglev railway in Germany called Transrapid, set to link Berlin and Hamburg by 2009, but political roadblocks have slowed the process.
One problem with maglev trains is their high cost. The price of all that electromagnetic material begins to add up, especially with longer tracks, and the improvement gain rarely seems to make up for the extra cost. Tracks have to be wider than those of conventional trains, to provide enough surface area for the repulsive force to support the train. A large benefit of these trains is that they have fewer moving parts than conventional trains, including a lack of wheels, meaning that maintenance requirements are significantly cut back.
Maglev trains have been theoretically possible for as long as there have been trains and magnets, but they haven't actually been implemented until the 1960s, when Japan built a test track. Britain installed a track at an airport around the same time, but it was replaced by a bus system due to the difficulty of procuring spare parts. It is questionable whether or not these trains are commercially viable at this time. As Germany is the only country with actual plans to implement a commercial system, and interest in the US has waned, Germany will be the world's testing ground for maglev trains.