As far as we can tell, it does appear to be true that the speed of light is the same for all observers. This fact was predicted by Maxwell when he united the electric and magnetic forces into one. From his equations it was possible to calculate that the resulting electromagnetic field travels at a constant speed relative to all observers. It was when Maxwell realised that this constant was the very same speed at which light was known to travel that he guessed that light was, in fact, electromagnetic radiation !
There is, as yet, no intuitive explanation to why the universe should act like this. Since Maxwell's work, numerous experiments have been performed to test the prediction that electromagnetic radiation travels at the same speed for all observers - and none have failed. Instead of being a prediction from theory, it now became to be used as an assumption to build theories upon. Einstein was so convinced of its truth that he modified Newton's theory of gravity to encompass the constancy of light. Likewise, in the 1940s, Feynman, Tomomaga, Bethe and others incorporated the idea into Quantum Mechanics. The resulting theories, General Relativity and QED, are probably the most accurately tested to date - and they require that the speed of light is constant.