How fast is the speed of light?

On one hand, it's pretty cool to look up at the night sky full of stars and realize that you're actually seeing millions of years in the past — since light doesn't travel instantaneously. On the other hand, it's pretty annoying to think that no matter how hard we look, we won't ever get to see what some alien on a distant planet is up to right at this very moment.

Scientists started figuring out that you could indeed measure the speed of light as far back as the 1600s, as demonstrated by Ole Rømer, who didn't come up with the exact speed at the time but did wear some really impressive wigs.

But even if we can measure light's speed, it's obvious that it's still pretty damn fast. Just how fast is it?