21st Century Perspective
In the 21st century, most communities don't like being called communes, in my estimation, which is at least partly due to the automatic assimilation with something like the Jonestown Massacre. More appropriate titles would be intentional community or ecovillage. That being said, there are over 1,000 in the U.S. and at least hundreds in other parts of the world, so, as you can imagine, there is a lot of diversity.
http://directory.ic.org is a directory of intentional communities.
Anyway, some are income sharing, some are not. In some, all people follow the same beliefs, while in others there is vast array of beliefs. Food choices can run the gammut also, ranging from vegan to vegetarian, to omnivorous, to raw food, raw meat (yes, raw beef)... and then there's the lovely urine therapy.
Some make decisions by consensus (everyone must agree), while some have leaders or democracies. They range in size from single digits to a thousand, although those are rare, and, some suggest, things get out of hand beyond a few hundred.
Each one is like it's own little world, which is quite fascinating. I plan on visiting more in the near future and I'll always cherish the first time I ever lived at an intentional community.
One person mentioned outsiders at school shuning the kids from the community. Well, the one I lived at, there was a very fascinating dynamic among the children, which was, essentially, a stark contrast to the above, in which pure-breds (people born there) were esteemed, kind of idolized by the other kids, although I think it was more of wanting to be as much a part of things as their pure-bred brethren. Very interesting.
Anyway, what you have to remember is that most contain a hundred or fewer people. Therefore, scale is something to think about in just about every regard. You mention trouble in paradise with regards to relationships, well, think about it... with the sheer number of people everyone pretty much knows each other's business for the most part. One bad relationship can have ripple effects throughout the community. And I've seen the devastating consequences, which can last for up to a decade even.
Where I lived, there were wealthy people, poor people and everything in between. Living styles ranged from having a bedroom only separated by a piece of plywood to someone having their own yurt or hut to people with fancier houses.
My suggestion would be to go visit one. Although what you can glean in a weekend pales in comparison to living there, it is still useful and a good experience, in my estimation.
Of course, my juiciest information is saved for my last writing project and my current one, but I actually just posted structural pictures
here.