I am currently working on a shawl for our local hospice. They are called prayer shawls, but there isn't really any religious significance. Our hospic is desperate for them...many of the patients no longer have family ties and this is something that makes them feel loved. A friend of mine is a nurse there, and she said that many ask to die in them... :(
I know our local fire department is always looking for teddy bears or blankets for families and children who lose their homes to fire (imagine the comfort that would provide to a child who just watched their house burn down!).
Our hospital accepts hats for preemies and infants all the time.
I didn't have time to look it up, but afghans for afghanistans is a great charity (and completely not picky). They accept hats, scarves, mittens, sweaters, and afghans to warm a nation struggling to rebuild.