Once, I was looking at reply slips received back from an acquisition mailing. One person wrote in the margins of the slip, "I am taking your word that you help people with this money."
I believe that most donors, especially first-time donors, feel this worry. But one person felt it so strongly that he wrote it in a message to us.
Donors give because they believe their money is going to make a difference. That new donor, who doesn't have a relationship with you yet, is going to feel concerned that she is throwing her money away. She needs you to convince her that she is investing her money into a worthwhile cause she cares about.
Neuromarketing has a blog post about words that build trust. Apparently, literally saying "You can trust us," well, works. Some of the other words aren't relevant to a nonprofit, like "fair price." But check it out, it's something to think about in your messaging, especially in your acquisition mailings.
This is also something to think about with regard to your welcome package—part of your messaging should be reassuring the donor that he made the right decision to donate (so he'll donate again!).