Non-profits

I am curious about the way developers handle working with non-profit organisations. Juste like a lot of organisations and people, they have a need for software and websites. But, they also might not have a budget anywhere near what is required to have what they want.

If a non-profit approached you to build something, what would it take for you to give them a hand? Assuming that the organisation's mission is something that resonates with you, would you be willing to lower your rate, or even do it for free? Are there things you are not willing to give up under any circumstances? Have you ever had any experiences like these?