I'm no accountant so forgive the shortcomings:
The simple answer yes, the long answer maybe;
Yes [though as Sushi implied if auditted you'll likely need reciepts to prove it legit, but the eligible organizations range from churches to universities and almost everything imaginable in between]; however:
at one end of the spectrum there is the "standard deduction" a single figure already assuming a modest combination of expenses and donations ect., so if you're using that, no you don't yeild further financial gain.
On the other end, I believe there are some limits, or at least some percent that would generate an audit.
Back to the simple answer, if you're expecing to pay at a 20% rate, then the donated amount [including value of material items and milage] would be that much less you'd pay on: yielding a 20% [not to mention potential gains from a lower bracket] reward.
Compared to the expense [even without waste] of beaucrats doling it out, I'd say the 'reward' is quite cheap for the federal government.
