Thanks to the members of firstname.lastname@example.org for your ideas. If you're ever trying to solve a problem and can’t quite come up with the right resource, this group is the place to go. Someone in this group of very helpful people always knows the answers.
Strawberry Canyon Blue Camp's Social Skills camp, on the UC Berkeley campus offers a program for kids with social skills deficits, grades 3 to 12. Younger kids are in groups with a leader, but take part in their activities along with the typical kids from the larger daycamp. For teenagers with special needs, the camp offers a counselor in training program, with focus on social skills as they relate to job skills.
Quest Camps in Alamo offers programs for campers from ages 6 to 18, with special responsibilities and programs for teen campers. They have daily activities, field trips and therapy.
Trails to Success offers their summer camp programs in Orinda. They also have a counselor in training program for teenagers.
Walnut Creek offers a summer therapeutic program through the city parks and recreation. We Care in Concord has also offered an autism summer camp, although I only found online information on the 2009 program. The Easter Seals Kaleidoscope program in Dublin offers an after school program, and I'm told they extend their schedule to longer days over the summer.
Sarah’s Science “This Land Is Your Land” camp is not designed specifically for special needs children, but the science and nature themes may be of interest to many kids. A mom told me that her son with Asperger’s really enjoyed the camp. Older campers can do more challenging projects, and there is a counselor in training program. The camp is located in San Ramon, Berkeley, and Oakland.
Tech Know How offers camps on computers, Legos and game design. Again, this camp is not designed specifically for kids with special needs, but it does match well with the interests of many kids on the spectrum, and a mom reported her child with Asperger's enjoyed it. They have locations throughout the Bay Area.