The speed at which sunlight travels is equal to the speed of light. Photons that are emitted from the surface of the Sun are forced to pass through the vacuum of space on their way to our eyes.
The short answer is that it takes the light from the sun an average of eight minutes and twenty seconds to travel from the sun to the earth.
If the Sun suddenly disappeared from the universe, it would take you slightly longer than 8 minutes to realise that it was time to start putting on a jacket because it was getting colder outside.