sogman A lot of users, myself included, use the heart icon to mark something as watched. That way we could instantly see if it was something we had viewed previously (whether you're looking for that, or more often the case looking for something you haven't watched previously). Along side that the old site used to list the total number of hearts a video had received, which was a great metric as to how much traction that video had.
I used to use the comments icon, with the total number of comments on a video, in the same way, and I lament that both of these icons are missing.
I have never used the watch later icon, however owing to various factors I find I need to download a video before watching it, so I guess in a way my harddrive/s are full of 'watch later' videos.