For now, the Diablo III beta is only accessible to Blizzard employees and their families, so chances are that if you are reading this, you probably haven't been invited yet.
However, the good thing about the beta is that, while not accessible to everyone yet, it is no longer under any NDA. Meaning that it's being freely broadcast over the Internet by some of the players. Here's a list of some of the places you can watch the game being played:
Let us know if you know any other such places! And help us fill the wiki with all the new information.