YouTube has a cool new feature in their labs. It's called Active Sharing and it lets you see other users that have enabled the feature and watch the same video as you. If you click on the username, you can see the profile and the last six videos they watched. This can be deactivated at any time, but it's pretty useful if you want to discover people who collect cool videos and subscribe to their channels.
In case it crossed your mind to use Active Sharing to track the videos watched by someone, YouTube says you can't. "YouTube respects your privacy. This information only shows to other YouTube users for 30 minutes, so get busy and show off your good taste!"