Update May 2009: According to the Foundation Center, corporate charitable giving is expected to drop by more than 10% this year. But try looking at it this way- even in the midst of the worst economic malaise in almost a century, American companies are still giving almost 90% as much as they did during the fat times. Kudos to them.
Private and public agencies that provide emergency assistance in cash are uncommon, and those that do usually restrict that largess to those well below the poverty level. However, many will provide other services and items that you would otherwise spend money on, so this charity could free up some dollars to apply to your other most pressing needs. Among the most common of these are food banks and open dining opportunities, help or waiver of utility costs, and clothing and other household essentials.
Your local government often has a person or office that acts as a clearinghouse for social services. Don't forget about churches and social clubs, too, who often have less formal outreach programs, especially for members in distress. You'd be amazed at the not-for-profit groups that are sitting on many thousands of dollars simply because no-one has asked them for some of it.