Wow. Where to start?
I took up crochet again, after an approx. 15-year hiatus due to Carpal Tunnel Syndrome, in January 2008. By the end of 2009, I had crocheted 30 chemo hats. These were turned in at a local yarn shop which donated them to a women's health center in Oakland (I think; maybe Berkeley).
Simply find a health center that deals with people who have cancer and get going. No shipping. Men, women, and children all face hair loss from chemotherapy due to cancer. Others face hair loss from neurosurgery, yet others from alopecia and additional medical conditions. Contact medical centers (oncology, hospital social workers, etc.) for guidance; there may be fiber requirements.
Similarly with infant needs. Neonatal Intensive Care Units (NICUs) often need an infinite supply of caps, tiny mittens and booties, blankets, and other items for the babies in their care. They will also have specifications for fiber and size of items.
I currently work with a group who knit/crochet hats and neck scarves for a homeless project in San Francisco and baby hats and blankets for a mother/infant hospital in Tanzania. We have these two diverse target delivery groups because that's where our personal contacts are. One of our members works directly with the specific homeless project in S.F., so she can verify that the hats and neck scarves are put into the hands of homeless men and women who can use them. The daughter of another member works at the Tanzanian hospital/clinic and can personally verify that the blankets and baby hats go to new mothers and their infants. The concern is for the items to make it to the targeted recipients and NOT to be diverted into a cash stream for third parties.
If these options don't work for you and the others, why not approach the social outreach officer (or whatever he/she is called) in the local police/fire departments? Often, children or even entire families are traumatized by the loss of their home in a fire, or children are suddenly taken from their families by Children's Protective Services (CPS). Children finding themselves suddenly in foster care can definitely use something made specifically for them like a blanket, pillow, teddy bear (maybe for younger kids), etc.
Warm Up America is a great way for individuals to pool their resources together. Each person can knit/crochet a 7"x9" rectangle, and the rectangles are joined into blankets. Give these away in your community through the WarmUp network or through the channels I've listed above.
No doubt many more members of Knitting Help will have yet other helpful suggestions; these are just a start. Most yarn shops (and quilt shops, too) know of many community projects their clients support, so call around locally, too.