I was pleased to be able to get started on this goal two weekends ago. The organization in this case was the Greater Chicago Food Depository. If you've ever volunteered time for a food bank, then you'll know that what they commonly have you do is package or re-package food for distribution to individuals. In this case we (myself, my girlfriend, and about 30 other people) were working on a project where we repackaged a dozen or so different foods into bags that were going to children in the Chicago area that receive free or reduced cost school lunches. The bags of food, once complete, are then distributed to kids for their weekend meals.
If you'd like to volunteer for a similar organization, there's tons around the United States and abroad. You can find more information at bread.org