Zenimax support confirms that there will be no “traditional open beta” for Elder Scrolls Online. Earlier Zenimax stated on Elder Scrolls Online’s facebook page that they would plan to conduct one. However, if you sign up to ESO beta before the launch and are eligible with the Terms of Service (mainly meaning you are of appropriate age), you are guaranteed to get an invite for future beta events. Oh, and there will be several, large beta sessions prior to launch.
This is as close to open beta as it gets, though. I’m going to call it closed open beta. I can only wonder why Zenimax decided to not do a traditional open beta, but one of the reasons might be the ESRB “Mature” rating. By having a *closed open beta*, they can monitor the testers, or rather, their age, slightly better.
If you still haven’t received a beta invite, you are very likely to receive one in the future. You can sign up for ESO beta here.