I just noticed that YouTube is showing off a brand new feature. When you are signed into your account, just click the button to add a video to a playlist. One of the "playlists" will be 'Watch Later'. Click it and YT says that the video has been added to your list.
This option is also available on videos embedded on other websites. For example, over here:
You'll see it when you pause it and/or move the pointer to its top. It will be in the same line as the one where the title displays (the dark band at the top).
After you save these videos, where do you see it? On your homepage. When logged in, go to your personalized YouTube homepage, and look around. You should see a new section saying 'Watch Later'.
Currently, that is, as I write this, the videos in the list don't get removed automatically after you watch them, but I'm sure this will be added soon enough.
Vimeo, the other famous video-sharing site also has had this feature since a few months ago. Good that YouTube is adding this too. Now you can save videos to see later if you don't have time to do that right away.