While YouTube doesn't track the dates and times of when you watch videos, it does keep a list of the videos you've watched. This means that the only way to find the exact date and time of your viewing is to check your browser history. However, this only works if you had history enabled in the browser you used when you watched the videos.

History Search

Open your browser's history, and then search the YouTube entries until you find the video in question. The history listing for the video gives the date and time of when you accessed the video -- unless, that is, you've cleared your browser history since you've watched that video.

YouTube History

Sign in to your YouTube account, and then click "History" on the left sidebar to see a list of the videos you've watched. The most recent videos show up at the top. Although this feature doesn't show dates and times, if you remember when you saw the videos before or after the one you're seeking information for, this can help you narrow the time frame.

Video Manager Search History

If you used YouTube's Search feature to find your video, click the down arrow to the right of your name and picture in the upper right corner while you're signed in to your YouTube account, select "Video Manager" from the drop-down menu, and then click "Search History" on the left sidebar to view your searches. The search history gives general time information, such as "2 hours ago" or "1 year ago."