There is, for example, Admission Day, the day the Republic of California was admitted to the Union as the State of California. We don't actually get that day off anymore; the holiday time that we're required to be given by law is used to give us the Friday after Thanksgiving off instead.
Our newest unique holiday (well, about 5 years old, I think) is Cesar Chavez Day. It's on March 31st, and we get the nearest Monday or Friday when it's on a weekend. Means that we've got pretty good odds of a 3-day weekend at the end of March.
This year the odds pay out again. It's next Monday.