Which country built the first steam locomotive to run on rails?

The first steam locomotive to run on rails was built in the United Kingdom. Richard Trevithick constructed an early full-scale locomotive at Coalbrookdale in Shropshire in 1802, followed by the better-documented Pen-y-darren locomotive in South Wales in 1804.

On 21 February 1804, Trevithick's Pen-y-darren locomotive hauled wagons of iron along a tramway from the Pen-y-darren ironworks toward Abercynon. The journey demonstrated that high-pressure steam could power a locomotive on rails, although the heavy engine damaged the relatively fragile cast-iron track and was not commercially adopted.

This answer is sometimes confused with the first commercially successful locomotive, Salamanca, built in 1812, or Locomotion No. 1, which hauled passengers on a public railway in 1825. Those were important later milestones, not the first rail-running steam locomotive. Trevithick's work helped launch the intensive locomotive experimentation that later flourished in northern England.