What is interesting is that this is viewed as such a novel idea! One church member said: "You don't hear about a church giving money away." I think it is a sad commentary on many churches, or at least on people's perceptions of churches, if a church giving money away is a rare occurrence. I do not know if that is true or not but for members of The Church of Jesus Christ of Latter-day Saints, a church giving money to others is nothing new.
One Sunday in every month (typically the 1st) is designated a day of fasting. Church members fast for at least two meals and are encouraged to donate at a minimum the money they "saved" on the meals to the church. This is not a requirement, no church member is required to pay a fast offering, it is simply encouraged. Of those who are able, most pay much more than the cost of two meals. 100% of this money goes to help those in need, first in the ward or branch (the smallest, local congregation), then in the stake or district (a collection of wards or branches), then in the broader church (although it might still stay in the general area - e.g., southeastern United States - first). The LDS Church has a lay ministry, which leads to a fairly small overhead (although the upkeep on LDS Church buildings is not "small" but the Church does not pay salaries to any of the local leaders). All overhead for these fast offerings (which overhead is quite small) is paid by tithing; this means that 100% of fast offering money goes to help those in need.
Isaiah wrote of the relationship between fasting and helping those in need: "Is not this the fast that I have chosen? to loose the bands of wickedness, to undo the heavy burdens, and to let the oppressed go free, and that ye break every yoke? Is it not to deal thy bread to the hungry, and that thou bring the poor that are cast out to thy house? when thou seest the naked, that thou cover him; and that thou hide not thyself from thine own flesh?" (Isaiah 58:6-7).
Separate from but related to this, the LDS Church has a large Humanitarian Services program that provides aid to those in need around the world. Tithing also pays overhead for this program, meaning that all money donated to LDS Humanitarian Services goes to help those in need.
Here's an example of the LDS Church's Humanitarian Services.
Here are a few statistics about the LDS Church's Humanitarian Services (these do not include tithing or fast offerings).
Humanitarian assistance rendered (1985–2008)
Cash donations $282.3 million
Value of material assistance $833.6 million
Countries served 167
Food 61,308 tons
Medical supplies 12,829 tons
Clothing 84,681 tons
Educational supplies 5,965 tons
Hygiene, newborn, and school kits 8.6 million
While the amount donated is impressive, what's important is that members of the LDS Church collectively and individually try to live the teachings of the Savior and honor His call to take care of our neighbors, wherever in the world they might live.