Like sports or arts and crafts and want to help children with mental and physical disabilities? Try KEEN (Kids Enjoy Exercise Now) for one-to-one sports, swimming and arts and crafts programs.
Looking for a soup kitchen? Check out this list of soup kitchens operated by the Coalition for the Homeless. Want to volunteer at the oldest and largest soup kitchens in Manhattan? Try St. Francis Xavier on Sunday late morning - early afternoons.
Have a special interest in food, hunger and/or nutrition? City Harvest is a wonderful organization that works to feed hungry New Yorkers and many of their programs do not require any long-term commitment. You volunteer when you can. I highly recommend the Mobile Markets, where you distribute food at community programs. It's a great way to interact with members of the community and see the benefit happening right in front of you. You've never fully appreciated the importance and privilege of access to good produce until you see someone's eyes light up over a what may appear to be just a few free potatoes, something many of us would probably take for granted. You've never savored the gift of life until you ask someone how they are doing and their response is, "Well, I'm positive," and it takes you a moment to realize that they're not talking about their sunny disposition.
Food Bank for New York City is another great organization with volunteer opportunities focused on hunger and nutrition.
Interested in helping domestic violence victims? Try Sanctuary for Families, or the Anti-Violence Project (AVP specifically focuses on violence within the LGBTQ population).UPDATE: I forgot to mention Safe Horizon.
Many local hospitals also offer opportunities to serve as a rape crisis, violence or assault counselor, after undergoing a lengthy training and committing to at least one year of being "on-call" one to two nights or weekend days per month. Here is a list (that could probably use some updating...) to get you started searching for these programs. Most hold training once a year, in the fall, and will start recruiting in the summer, but some have different schedules. I know that NY Presbyterian/Cornell Medical Center on the UES, and Wyckoff Heights Medical Center in Brooklyn are both recruiting now for training that begins in the spring.
One group I learned about recently, while looking into domestic violence organizations, is Camba. This non-profit organization encompasses much more than providing assistance to domestic violence victims. Camba has six "core" areas: Economic Development; Education and Youth Development; Family Support Services; HIV/AIDS Services; Housing Services and Development; and Legal Services. You are bound to find something interesting under one of those categories.
If you're Jewish, single and 28 years old or younger (strange parameters, I know, but it's a fun group), try jcorps. Their motto is "make friends, make a difference." Group volunteering events vary from week to week but may include doing arts and crafts with seniors, beautifying parks, spending time with children at a pediatric hospital, and more. Jcorps is actually how I learned about St. Francis, and also another group, the Metropolitan Council on Jewish Poverty. Don't be fooled by Met Council's name. The organization serves Jews and Gentiles alike, and any person of any faith (or no faith) can volunteer. Met Council literally has an endless list of programs.
Are you a lawyer or in the legal profession? Check out Legal Outreach, which helps prepare urban youth for college and grad school.
Are you a singing lawyer or legal professional? Audition for The City Bar Chorus. CBC's "primary mission is to reach out to the community through music." The chorus sings at community venues across the city, including senior residences, rehabilitation facilities, cancer centers and more. I also have it on good authority that they may be looking for some tenors and bases right now...
Like animals? The Bronx Zoo, Queens Zoo, Central Park Zoo, Prospect Park Zoo and New York Aquarium, which are all run by the Wildlife Conservation Society, have various volunteer opportunities, as does the Staten Island Zoo. Most of these require a long-term commitment.
Feeling political? There are likely volunteer and outreach opportunities available within whatever party you support. Try the New York State Democratic Committee or the Republican Party of New York State, or if you're a young professional, try the New York State Young Democrats (I have personal love for the Manhattan Young Democrats chapter) or the New York Young Republican Club. Independent? Libertarian? There's something for you!
Also, don't rule out your local house of worship, even if you're agnostic or atheist! Synagogues, churches and the like offer many varied volunteer and outreach opportunities, which may be more secular than you'd expect (e.g. Brooklyn Heights Synagogue runs a secular women's shelter November through March, in cooperation with Camba).
If none of these appeal to you, you can conduct your own search for whatever opportunity may suit you at a number of different websites:
New York Cares
Idealist (non-profit job and volunteer search engine)
Volunteer groups on meetup.com
And finally, anything and everything else you could possibly ever want to do for others you can probably find at nyc.gov's volunteer site.
UPDATE: Another search engine - volunteermatch
Now, get out there and Do Something!