cwilbur is right, speed depends on a frame of reference, from your reference point in the spaceship, the light would appear to be moving at the speed of light
@rogy, the speed of light is a constant (given that the constant is different based on what the light is moving through, like 8lightminutesaway points out)...but its way more complicated than that
this is one of Einsteins fundamental postulates of special relativity, that light propogates at the same constant speed regardless of any motion of its source or motion of the observer. Light travels at c relative to the observer. Always.
It has to do with the relative stretching or contracting of the time and space dimensions that occur when you move. You will observe space and time differently than an observer moving relative to your frame of reference.
An example of this, if you hold two clocks in your hands and they show the exact same time, then your friend takes one clock up in a plane and flies around the world while you hold the other clock in your hand, when your friend lands back in the same spot, comes out of the plane and puts the clock back in your hand, they will read different times.
Decent explanation
@brownlemur, Brian Greene is a good explanation
also, if you like math, look up Lorentz transforms