Heifer International is my favorite large charity. I like their "teach a man to fish" approach and how many different options there are for giving. They get full marks from the BBB on their accountability standards.
I've given Heifer donations as gifts, too. The last 10 years of my grandmother's life I gave her a gift donation of different animals each time. She was at the point where she really wasn't interested in the usual bday tsotchkes, so she really loved knowing the money was going to a great organization and looked forward each year to seeing which animal I'd pick.