Here's a tip to quickly find and watch videos others have shared on Twitter.com, simply scan your timeline for Tweets marked with the filmstrip icon. Clicking the icon will open a details pane beside your timeline in which you can watch the video.
Want to share a video and give others an excuse to take a so-called "YouTube" break in their day? Just use YouTube's sweet and simple link shortener. Grab the video ID (that jumbled set of letters and numbers in the video's URL on YouTube) and insert it into this little URL: http://youtu.be/[videoID] These types of links will display the video in Twitter's details pane, and will mark your Tweet with the filmstrip icon.
Watch in action in the video below: