There are several not-for-profit e-mail servers, but most are not free. Vertical Response has a free version for nonprofits but I don’t know anyone who uses it so I can’t give you feedback. Most of my NGO friends use Constant Contact. Many of these providers use a sliding scale for nonprofits depending on size and budget, so you may find one that’s more affordable than you think.
Here’s an article with advice from Idealist.org, which is a useful site to subscribe to (once they’re done with their site relaunch). And finally, here’s some good general advice about nonprofit e-mail from a friend of mine. She gives the names of a couple more services which, unfortunately, aren’t free. But you should subscribe to her blog and e-newsletter for general advice about promoting your NGO.