Yes, you can play Words with Friends on Android, iOS and Facebook. The most accessible way is the Facebook way. Access the application using the official URL and you'll have the possibility to play it. However, the Zyngo Toolbar is used to access the games easily without visiting the addresses each time. In this case, the toolbar has no use since it doesn't provide a quick way to play the game.
You need to have a Facebook account in order to play it on your computer.