What is the role of the nonprofit sector?

In my inaugural post to this blog, I would like to begin by offering a big question, why does the nonprofit sector exist? What is its global role?

The question is not purely academic, but one related to a number of issues being raised about the sector these days including:
1) Are there too many nonprofits? As discussed in today's NYT, there are over 1.1 million nonprofits registered in the United States. This have led some to decide that there are too many nonprofits (see this debate in the Blue Avocado nonprofit blog) and others to question whether what nonprofits do should free them from paying taxes. Many wonder, can the government do what nonprofits are attempting better or more efficiently?
2) One of the new trends/fads in the social sector is the for-profit social enterprise. Proponents argue that for-profit business models allow for the scaling-up of social impacts in ways that are not possible in not-for-profit models. Detractors argue that for-profit models work only for some social problems (e.g., microfinance) and that in such models values and profits may conflict. For more, see this podcast for an example of 1 year old social sector organizations using both for-profit and not-for-profit models.
3) A growing number of government-nonprofit and corporate-nonprofit partnerships have arisen in the past decade. For example, intergovernmental organizations, like UNDP, rely of nongovernmental organizations to accomplish development goals. New corporate-nonprofit partnership forms, including nonprofit certification of corporate practices and cause-marketing, have emerged. Critics argue that governments and corporations may co-opt nonprofits making them less distinctive.

So, here is the questions that I hope to investigate. What is the distinctive role of the nonprofit sector? What can nonprofit organizations do better than governments and for-profit organizations? Feel free to weigh in and offer suggestions. I will take up suggestions in future blog posts.