For two years now, I've alternated "giving knitting" with projects for custom orders and myself. At first, I worked primarily on prayer shawls. The first thing I ever knitted was a prayer shawl, knitted through the long nights in the pediatric ICU while my son fought septic shock and other complications from Crohn's Disease. I've kept that one, and given every other one since to Children's Healthcare at Scottish Rite, to give to moms in the same situation. Those ICU rooms are freezing, and there's nothing like a tangible hug that warms you inside and out. That's the power of a prayer shawl. My two favorite patterns are also the easiest:
For a "trinity" patterned shawl: Cast on 99+ in any yarn, any needle size of your choosing. Knit in K3 P3 ribbing until shawl reaches from fingertip to fingertip. Add fringe. Say a prayer. And give it away.
For a triangular shawl (three sides = Trinity), follow "Grandma's Dishcloth" pattern: Cast on 4 stitches with any yarn, any needle size. Turn. Knit across. Turn. Knit 2, YO, knit across. Continue K2, YO, knit across until shawl is large enough to wrap the recipient warmly.
Then, my knitting circle started making layettes for Share Atlanta, a bereavement support group for parents of children lost during pregnancy. (Their web site, http://www.shareatlanta.org/. has lots of wonderful background information.) I had personal reasons for participating in this "giving knitting," so have tried to make at least one set of blanket, booties, & hat each month.
I've added a link to CareWear, which has the best set of patterns I've found for these ultra-tiny gifts.