You no longer need an invite to check out the new Google Maps. You can get it immediately by going to maps.google.com/preview.
Daniel from the Google Maps team said in a Google Maps Help thread:
In May, we unveiled a preview of the new Google Maps for the web, and today we're making it even easier to try it out. You no longer have to request and wait for an email invite – just sign up and get access instantly at maps.google.com/preview
For those who have already taken the new maps for a test drive, thanks for all your support and feedback. We're listening and continuing to make the experience even better. Please continue to let us know what you think via the "Help and Feedback" button in the top right corner of the map. For those who haven't tried it yet, here's a refresher on what makes the new Google Maps great: http://youtu.be/THxJHcR1D2c
There are many features you may be accustomed to that are not yet available on the new Google Maps. One such feature is adding a 3rd destination or more to your directions. So keep in mind, this is a preview only.
Forum discussion at Google Maps Help.