Here are several different ways that tweets with links to videos are handled. The experience will be vastly different depending on which method you use to access twitter. I will use the same tweet involving a link to the song “Pure Imagination” from the movie “Willie Wonka and the Chocolate Factory” (one of my faves BTW).
Here’s the tweet from @CraftyChica as it appeared in a traditional browser from twitter’s home page.
Everyone knows you have to click the link in order to see what she was referring to. However, it could be an audio link or a video. The only way to know for sure is to click it which will then take you there either on the same page or in another new tab.
Here’s the tweet as viewed from TweetDeck, one of the most popular Twitter clients 
It’s basically the same deal. Click the link and the page opens in your browser.
Here’s the tweet from a browser infused with the new PowerTwitter add-on. 
Now this is better. It’s obvious now that she has shared a video from YouTube. Wonderful! Or is it? When you click the play button the video does NOT play! Instead, it merely takes you to YouTube to play it. So, basically, it’s only a visual clue as to what it is. Still, it’s a step in the right direction. However, it’s close but no cigar for video fans like me.
OK, here’s the same tweet from Tweetree, an alternative web-based client for twitter.
While it appears just like PowerTwitter, it isn’t! When you click the play button guess what happens? Yup, it plays! It doesn’t take you to another page or YouTube, it begins playing right there in your Twitter stream.
But wait, there’s more! Tweetree does the same thing with many other forms of media. For example, here’s how it handles blip.fm songs that are tweeted. Notice how it shows information about the song and what the user’s message and the play button.
Final Thoughts
I think the future of tweeting and all online communication is going to be more graphical like this. It not only saves time but only adds to the experience. Some other services such as Plurk and Rejaw do a better job than twitter when it comes to playing media in their streams but Twitter is much more popular and has a far greater audience. Let’s hope Twitter decides to provide support for playing media within our tweet stream.