YouTube automatically keeps track of your browsing history and marks such videos as already watched. However, such a mark is removed after some time, which may not be to everyone's liking.
Watchmarker for Youtube for Chrome and Firefox solves this problem and automatically marks the watched videos on YouTube automatically.
In the extension's settings, you can import or export your browsing history, as well as manually start synchronizing this list with data on YouTube or browser history.
Also in the settings, you can specify the conditions under which the video will be considered viewed and the style of marking the fact of viewing.