It is not yet confirmed but seems that Diablo 3 beta is free to play for everyone at this moment.
This notice was posted on a few gaming forums and also two hours ago on the official Diablo 3 forums on this topic.
Everyone can login and play using their battle.net login details after downloading the Diablo 3 beta client from here.
This works for both Europe and United States even though the url comes from us.media.battle.net.edgesuite.net (us).
The users that posted on that forum thread are confirming that they can login and play the game without a beta invitation received for their battle.net account.
Nobody knows for sure if this is just a bug and Blizzard will fix this situation as soon as possible or is just a way that they are making the beta public and everyone can play the game for a few more days until they will shut down the servers and delete all the beta characters.
On other forums, some users said that the beta isn’t available for those that already pre-ordered the game. If this happens, create a new battle.net account and login using those new credentials.