In California, tree law spans six different civil codes in addition to common law and local ordinances. You could get into a lot of trouble for trimming a tree that doesn't belong to you, or even cutting down one that does.
Your neighbor is not allowed to grow his tree onto your property. If he does, however, you are not allowed to trim the offending roots or branches yourself. First ask your neighbor in writing to trim the tree. If your neighbor doesn't comply with your request, then complain to the city about the trespassing tree.
You must maintain the trees on your property in a manner that prevents them from becoming a hazard. You need to trim your trees regularly, in a manner that preserves their structural integrity. Allowing your trees to grow unchecked or trimming only the big branches could result in them falling and injuring someone.
Oak trees, redwoods and manzanitas are protected by California state law. Under no circumstance are you allowed to cut or trim a manzanita. It is also illegal to own a manzanita branch.