I've been asked that question a lot, too. Actually, not so much as a question but as a statement, "Oh, I only give to nonprofits that have less than x% overhead. I mean, really, the money should be going to the people being served, right?"
Well, sort of. Here's the catch... everyone (and I mean EVERYONE) fudges those numbers. Here's how.
Take nonprofit X, which has several programs. Those programs serve people, or save things, so all of their expenses are considered "direct" and are not considered overhead. However, those expenses do include staff and paper and office space, etc., because you have to have staff and paper and an office to run the program. It's not like people who work for homeless shelters are handing out money to the people they serve. No, they are providing a service TO those individuals.
So you see the problem... where do you draw the line? Only at the direct line staff? How about the manager that oversees the line staff, but is needed to provide the relationships to other nonprofits, set the strategic direction and raise money? What about the paper... if we purchase it in bulk at the main office, can we distribute and expense it at the program level and not have it count towards overhead? ABSOLUTELY!
That's what happens. To the extent possible, costs are allocated down to the program level where they don't "count" in official overhead reporting, even if that includes multiple layers of management, parceled office space, etc. (My program had to pay for my own cubicle at a nonprofit, which, of course, was considered a program expense when reported because I, as a Program Director, was sitting there).
This is where I step in and say "Forget about the overhead!" That's actually what you are paying for... your donations are going to support an organization that does great things. But to do those great things, it needs resources spent on unsexy things like staff and office space. When deciding on where to donate, instead of jumping straight for that overhead percent, I find it more helpful to look for things like their mission... does it resonate? What success stories do they publish about how their programs affect lives? Do you have friends or relatives that are affiliated with the organization? Where have I been helped in my life, and does the organization help others in a similar situation?
When you find the answers to these questions, you will have found a great place to give - something that has meaning, and resonates with your experience and values. And in doing so, you'll know that you're helping to make the world a better place... by paying for the staff (and paper!) that serves the people, animals and places you'd like to help.