I think there are four things that make a good charity website:
A clear mission statement. What does the charity do? What is the mission of the charity? A clear statement of the charity's goals right up front tells potential contributors what they need to know before they (potentially) donate.
A "running tally" of who has been helped. List that "x millions served" number, like McDonalds used to have on their signs. It gives visitors an understanding of the impact the charity has.
Where the money goes. I'm big into transparency, so a chart or listing that details how much of donations goes directly to those in need vs. administrative costs will go a long way convincing me (and many others) to contribute.
An easy way to contribute. Make it simple and easy for people to donate money. Integrate with Paypal and other payment services, and make the "check-out" form simple and easy to use.