Some favorites of BPC families:
Monkey Business (at Berkwood Hedge)
Sarah's Science (in Tilden)
Kee Tov (in Tilden)
Ha Ha This a Way (West Berkeley circus, martial arts...fills fast!)
Camp Galileo (younger kids) & Summer Quest (science, art, games, 5th-8th graders) various locations.
Chabot Space & Science Camp (3rd-7th graders)
Berkeley City Camp
Camp Kala (exquisite arts camp for 1st-8th grade)
Berkeley City Camp
Camp Kala (exquisite arts camp for 1st-8th grade)
on the geeky side:
ID Tech (ages 7-17, at UC Berkeley: game design, programming...)
Robotics for Fun (Piedmont & Mountain View)
Berkeley Chess School & Galaxy Robotics
Robotics for Fun (Piedmont & Mountain View)
Berkeley Chess School & Galaxy Robotics
Got more ideas? Add 'em as a comment!