Other than the famous mad kings of Bavaria (i.e. Ludwig II and his brother, Otto, who nominally succeeded him), some examples coming to mind would be Czar Ivan V of Russia (the elder half-brother of Peter the Great), Prince George of Serbia (eldest son of King Peter I Karageorgevich, older brother of King Alexander I), and Emperor Ferdinand I of Austria.
Juana la Loca of Castile might count, since she was allowed to briefly rule the kingdom she inherited from her mother, Queen Isabel I. But between them, her father, husband, and son eventually took over. And, of course, she was not allowed to inherit -- much less rule -- her father's kingdom of Aragon. Instead (I believe), she got bypassed in the succession in favor of her son, Holy Roman Emperor Charles V.
I'm sure there are many more cases. Can anybody name them?