The United Fund and United Way mentioned above are "umbrella" charities whose main purpose is to prevent many major charities from having to make individual solicitations. A donation to one of these will be parcelled out by a local committee, so that many charities receive part of the funds. In some cases you can express a preference or exclude a specific charity to which you object, but it's questionable whether such preferences have much effect on the total received by each organization.

There are a number of organizations that claim to have information on the budgets of major organizations, in a form you can use to compare the "effectiveness" of your donations. I don't have notes (that I can find) on the oversight orgs that have been recommended in local news, but Google shows:

GuideStar purports to have IRS Form 990s for many charitable organizations. A registration appears to be required to view them, but the FAQ at this link indicates there is no charge to view them. Memebership may be required to get more than the most recent 990s for an organization. Religious charities may be exempt from filing the IRS Form 990.

CharitiesDirect appears to offer similar informatin for UK charities.

I can't vouch for these two as being the most "authoritative," but a quick search will find several similar organizations.

John