(covers information from several alternate timelines)
Insanity, craziness, or madness were terms used to refer to certain behaviors considered to be abnormal and against societal norms. The terms were also used to refer to a person exhibiting mental instability. Someone believed to exhibit such behavior was referred to as being insane, crazy, or a madman.
In 2152, Trip Tucker caught members of the Takret species having a barbecue next to a plasma manifold aboard the Enterprise NX-01. While Tucker understood the crew were explorers who were supposed to keep an open mind about different cultures, this alongside the Takret only needing to sleep once a week and keeping up the crew with strange rituals, chanting, walking in circles, and practically taking over the compartment were several reasons Tucker cited for driving him crazy. (ENT: "The Catwalk")
That same year, William T. Riker performed the role of the lead character in Beverly Crusher's play Frame of Mind, an individual in an abusive mental hospital who had been accused, possibly falsely, of murder. When a psychologist, played by Data, told him that he was becoming agitated, he replied, "You bet I'm agitated. I may be surrounded by insanity, but I am not insane." (TNG: "Frame of Mind")
In 2370, Worf proclaimed his belief that Iyaaran Ambassador Byleth was insane after serving as his guide during a visit to the Enterprise-D. Worf believed this after Byleth did nothing but exhibit antagonism towards him, which he did not know was actually a deliberate act designed to learn about such behavior. (TNG: "Liaisons")
The following year, Rom speculated that Grand Nagus Zek was insane after he wrote a revised version of the Rules of Acquisition. This version was based on less selfish and greedy principles than those that normal Ferengi society held. Quark dismissed Rom's speculation by stating that Zek was too brilliant to go insane. (DS9: "Prophet Motive")
In 2373, Gul Dukat asked Weyoun if he was insane after he drank a bottle of Kanar laced with Voraxna poison which had been intended to assassinate Tekeny Ghemor. Weyoun pointed out, however, that Vorta are immune to most poisons. (DS9: "Ties of Blood and Water")