|August 4th, 2013
In the US you can report money you donated, and for tax purposes that money is treated as if you hadn't earned it. While this does decrease the amount you pay the government, you don't come out ahead financially compared to not donating.
Let's look at an example. The median family pays taxes at a marginal rate of 15%. That means that if their income were to go up by $1K, federal taxes would go up by $150. If instead of keeping that $1K the family donated it  they could "deduct" $1K from their federal income. This would decrease their tax bill by $150, putting it back where it was before.
(This is particularly strange because people focus on their tax break and not the actual effects of their donation. For example, this CNN article writes that "Thousands of Americans who donated to charities last year in the wake of Superstorm Sandy and the school shooting in Newtown, CT. may not get the tax benefits they were expecting" instead of "Thousands of Americans ... were duped into donating to scams." Of course it's bad that these donors ended up spending $X when they thought they were spending 85% of $X, but that shouldn't be the main story.)
 This is only fully true if the family was already itemizing donations. If you don't have anything else you can deduct then you have to donate more than the "standard deduction", about $6K/person, in order to have any tax benefit from donating at all.