Reportedly, Google is occasionally allowing users to simply sign on to the service if they check the website at the right moment. Additionally, existing Google+ users (and that includes us) are sometimes seeing the ability to invite new users to Google's answer to social networking mainstay Facebook.
Earlier, Google shut down the ability of existing Google+ users to invite others. They did so after "insane" demand.
Now, although Google is still cautioning existing users to "invite carefully," current users are seeing windows in which they can invite other users open up more often. Not only that, the length of time that the invitation windows are open are being increased, too.
Notably, Google is still restricting the number of users that can register in a given window, so it's possible you might not be able to register, even given an invitation. That said, eventually, given an invite, you should be able to get in.
Rumor is that Google will open Google+ to all on (or by) July 31st. Given the demand for invites, it looks like Google might have gotten it right (social) this time. Time will tell if the interest is long-term or not