The parasympathetic aspect of the facial nerve controls secretion of the sublingual and submandibular salivary glands, the lacrimal gland, and the glands associated with the nasal cavity.
The vagus nerve, named after the Latin word vagus (because the nerve controls such a broad range of target tissues - vagus in Latin literally means "wandering"), has parasympathetic that originate in the dorsal nucleus of the vagus nerve and the nucleus ambiguus in the CNS.