Fans of Draw Something can play the game online on Facebook.com. The app has 28,500,000 monthly active users, and this number is increasing daily. The best part of playing Draw Something Online is - you can play with your friends across platform - this means you're able to guess your friends touchscreen drawing on your computer - it's led to the game's big success on Facebook, where it's currently getting 10.8 million daily users - a number that's even bigger than Words With Friends (by Zynga).
To play Draw Something Online, all you have to do is signup for a Facebook account. You can then head over to their games page, https://www.facebook.com/games, and choose Draw Something. The app will produce a list of friends who are also playing, you can easily pick an opponent and start you game.
Another way to play Draw Something Online, if you do not have a Facebook account, would be on the game developer's website, http://www.omgpop.com/#/arcade/gamelobby/drawmything. Hitting the play now button will automatically connect you to a lobby, in it, you can invite your friends by tweeting or emailing them a message and a link. The rules are still the same, but instead of drawing on a touchscreen, you'll have to use a mouse or the trackpad.
Here's a video of people playing Draw Something Online, (warning: may contain explicit languages and drawings)