For "to wake up" (as a verb):
* despertar (formal)
* levantarse (informal)
For "wake" as a noun (referring to the state of being awake):
* vigilia (formal)
* despertar (informal)
For "wake" as a noun (referring to a funeral vigil):
* velatorio
Examples:
* Me desperté temprano esta mañana. (I woke up early this morning.)
* Levantarse temprano es difícil. (Getting up early is difficult.)
* La vigilia de la reina duró toda la noche. (The queen's wake lasted all night.)
* El velatorio será en la iglesia. (The wake will be at the church.)