Some reliable and well known organizations that specialize in volunteerism are listed here
http://www.collegeboard.com/student/plan/high-school/7813.html
I volunteered at the Red Cross in NYC for all of high school and loved it. I'm in college now and I still volunteer with them. Because they're such a large organization, there are many different departments that you can request to volunteer with.
I've also volunteered with Housing Works in NYC. Specifically, I volunteered at the bookstore. It's such an untraditional place to work and I really enjoyed that too and plan on returning some time soon for weekends.
This also looks really cool, though I've never done it before: http://www.rooftopfilms.com/jobs.html