Colonization of the Moon
If multiple bases were established on the lunar surface, they could be linked together by permanent railway systems. Both conventional and magnetic levitation (Maglev) systems have been proposed for the transport lines. Mag-Lev systems are particularly attractive as there is no atmosphere on the surface to slow down the train, so the vehicles could achieve velocities comparable to aircraft on the Earth. One significant difference with lunar trains, however, is that the cars would need to be individually sealed and possess their own life support systems.
Monorail
Magnetic levitation train (maglev) systems by the German Transrapid were built as straddle-type monorails, as they are highly stable and allow rapid deceleration from great speed. At speed, maglev trains hover over the track and are not in physical contact with it. The maglev is the fastest train of any type, the experimental SCMaglev having recorded a speed of . The commercial Shanghai Maglev Train has run at . However, the guideway is so wide that it can be argued it is not legitimate to call it a monorail. 
There are also slower maglev monorails intended for urban transport, such as Japan's Linimo (2003).