That big Hangouts update wasn't just about making it prettier and finally rolling in Google Voice. Google also continued its efforts to make Hangouts independent of Google+, as it previously announced. You can now make multi-way video calls without a Google+ profile on Android.

As of the most recent update, users without a Google+ profile will be able to do the following via the app.

Start Hangout video calls with up to 15 participants

Include any external guests who have a Google account

Add, change or join a video call in a Google Calendar entry

Join or start a Hangout by URL or at g.co/hangout/ (and g.co/present/ to just present)

The last movement on this front was back in June when Google changed the behavior of user profile pics in Hangouts. They used to open the Google+ profile, but now they pull up a contact card. The new version gives those who don't want anything to do with Google+ a reason to take another look at Hangouts. It's not a perfect solution (just watch the AP podcast live and you'll see), but it's still probably the easiest way to get a group video chat going.

[Google Support: 1, 2]