The Squirrel Nut Zipper is a classic candy that I only recently had any contact with. Seems as though it's not really a California thing. Of course, we've all heard of the band by this name, but I didn't even initially realize that they were named after candy.
This is an older wrapper from the time that the SNZs were still being made by Squirrel Brand in Massachusetts. They are now being made by Necco.
I've attached a close-up of the rather dopey-looking squirrel logo. It's great. I've had a lot of mixed experiences with stupid squirrels, including one in which I caught a squirrel with one leg in, one leg out of my window, holding the screen open, about to raid my house. Love 'em or hate 'em, they're always amusing!
Check out the band's page about the candy's history. You'll find a cool video, radio jingles, and some fun anecdotes about how the wacky candy name came about.