As many have mentioned, the best thing to do is to get involved with an organization or cause that you care about. If you actually work with the organization, you will a) be helping them out significantly with your time and talents, and b) have a better feel as to whether they are using the funds they receive responsibly. I am on the board of directors of a mid sized (roughly $3,000,000/year) 501(c)3, and I know precisely what our overhead is. I also volunteer heavily for said organization (primarily network design, and electrical type work), and donate when I can.
Despite what other people say, any organization that is viable will have overhead. It costs money to ensure the books are properly kept and audited, there are bills to pay, and non-profits of all organizations, should pay their employees a fair and reasonable wage. From a financial point of view, the real key is to ensure that the books are properly kept, and there are adequate controls in place to ensure that the money is spent in an appropriate manner.