Anger is an emotion, a feeling of extreme displeasure.
Antiquated Earth religions consider feeling angry a sin against deity and unhealthy for one's eternal soul. (ST novel: The Unhappy Ones)
Anger and intense frustration or dislike are the cure to the plant spores infesting Omicron Ceti III. (TOS episode: "This Side of Paradise")
Kelvans realized how prone their new, human forms were to anger. James T. Kirk made this point clear after provoking Rojan into annoyed hostility (with underlying jealousy for his advances to Kelinda). By the time they hypothetically reach Andromeda, their Empire would meet their "savage" descendants. (TOS episode: "By Any Other Name")
Prolonged exposure to unstable Tholian space results in damage to humanoid brain tissue. This leads to angry fits of rage, paranoid insanity and death. (TOS episode: "The Tholian Web")
Besides fear, anger is a powerful, primal emotion. Entities have been known to feed off it and agitate more in order to become stronger. (TOS episodes: "Wolf in the Fold", "Day of the Dove")
Acts of wrath, vengeance or retribution have also been attributed to this often violent emotion, when one feels betrayed and unjustly treated. (TOS movie: Star Trek II: The Wrath of Khan; TNG episode: "Reunion"; TNG movie: Star Trek: First Contact)
Data, while on an away team mission to Ohniaka III, killed a Borg drone that attacked and thus angered him. (TNG episode: "Descent")
In strong telepaths, unmanaged, withheld anger can be contagious as disease to passersby. (TNG episode: "Sarek")
Anger is one of the negative emotions stimulated by the low-energy waves of certain harmonic diamonds. (TNG comic: "Captain's Pleasure")