The record speed of a steam locomotive is 126 mph set by the Mallard A4 steam train in Great Britain. The record was set in 1938 and still stands today! 2013 is the 75th anniversary of this world record.

There is no limit (in theory) as to how fast a train can run; it depends on how much acceleration the steam engine is capable of generating and how little friction the train has to deal with. I don't know the specifics for individual trains, but I don't believe historical steam engines as going much (if any) faster than automobiles, probably less.

The fastest steam train recorded travelled at 126 miles per hour.