I have given to the American Red Cross because they helped with the timely notifications when my dad died but if you want your donations to truly be effective and efficient, donate to the Salvation Army or even a Mormon temple. My dad worked for our state's Civil Defense department (essentially state-level FEMA) and he said the Mormons were far more timely and effective than the Red Cross. Whenever we had a disaster, the Mormons were on scene immediately with food, blankets, clothes, etc. while the Red Cross was on the air immediately asking for monetary donations.

EDIT: I am not Mormon or affiliated with any Mormon temple or organization. I don't buy their religious precepts but I respect their service to others.