The Buddhist concept of "community" depends always on a larger context. For most, there is a fairly identifiable 'spiritual community' consisting of those individuals that one meets with regularly and whom share common spiritual ideals. There is also an everpresent physical community, consisting of our neighborhood, section of town, or whole city. On the grander scale, there is the sentient community: every living being capable of experiencing suffering.
In the time of the Buddha, a relationship existed between lay persons and religious people. These religious people consisted of two categories: the dominant Brahman/Priests and the tiny sub-culture of renunciate wanderers (sramanas). The Buddha, when he was simply Siddhartha Gautama, left his life to join the wanderers. The community he created was likewise one of wanderers, though it would not be long after his death that the first permanent Buddhist establishments would come to being. In either case, however, the monastic community, the renunciate followers of the Buddha, were dependent upon the lay community for all that they had (as renunciates it would make no sense for them to own much!).
The Patimokkha...
From the "Buddhism is..." page (7 May, 2005):
Third is the question of whether Buddhism is community oriented. Here is one area where looking at the historical context is more helpful. Buddhism was born out of renunciates, people who completely gave up on society, dropped out, and sought higher realization on their own or under other renunciate teachers. In the society of the time, people openly supported such renunciates (cf. ancient Greece - you never know if the beggar at your door is an incarnate god), so as long as the renunciates didn't get into trouble or put too great a strain on the resources of a community, they would be looked after. There is evidence that with the rise of various schools of thought/religions in ancient India, there was indeed some strain on resources and renunciates needed to compete (to some extent) for food and support. In a sense, the community (lay people) relied on the renunciates for 'spiritual capital' in the same way that the renunciates relied on the lay people for 'material capital'.
In the present day, we can see similar tensions in who the laity support. Today in America most lay support probably goes to secular projects, which is in turn meant to support the people, bypassing religious hands altogether. Much also goes to religion though, by way of donations, tithing, etc. One thing that I believe contemporary Buddhists need to work on (and many, many are already) is benefiting the world around them. It is important to look to the building of shrines and temples and all of this, as these are good to expose people to Buddhism, but simple projects such as food kitchens, clothing donations, etc. will help to broaden the impact of Buddhists in communities.
Ultimately, each of us is urged to identify the pain of others as though it were our own pain. See Santideva's "Guide to the Bodhisattva's Way of Life". We must eventually see the suffering of others as though it were our own and take measures to help, just as urgently. Of course, as Santideva realized thirteen hundred years ago, one doesn't leap from self-centered delusion to social activist all at once. First we must being small, with carrots and potatoes (ie. start by giving small things away, things that you wont regret giving: a dollar a day or week, old clothing, old books, and carrots and potatoes).
See the whole "Buddhism is..." essay.