It turns out that you can automatically jump forwards and backwards in a YouTube video by pressing the number keys, 1 to 9. It only works when the video is paused or just about to start, not when it's playing. Pressing 4, say, will take you to the 40% mark in the video. And it's really quick.
On my PC it only works for the normal number keys, not the ones on the numeric keypad. However, in verifying that just now, I've also noticed that you can also use the arrow keys and Home/End to navigate through a video.
Now if there was only a shortcut to Pause a video.