Stun

Stun is generally regarded as the deadliest of status effects, as stunned characters cannot take any action, including blocking and tagging out, and Cloak of Destiny enormously increases damage dealt against stunned opponents

Batman's basic attacks deal greatly increased damage against stunned opponents.

It is not possible to have combo enders on a stunned opponent.

Red Son Green Lantern and Beyond Batman's passives provide immunity to stun, including stuns caused by Martian Manhunter or Luchador Bane's passive. Previously these stuns will ignore immunity, but this was fixed in an update.

Characters than can stun are Luchador Bane, Batman, Cyborg, Hawkgirl, Martian Manhunter, Prime Solomon Grundy, Static, New 52 Flash, New 52 Green Lantern, Killing Joke Joker and Zatanna (self-stun only).

Batgirl have visual stuns at the beginning of their Special 1, Art of Deception, but since it is the beginning of a special it only serves to trigger Cloak of Destiny.

Trivia

 * It is possible for a freeze special to apply stun through stun gear; there seem to be two outcomes when this happens: both "Stunned" and "Frozen" appears, and the freeze animation is played, or only "Stunned" appears and the stun animation is played. The bonus damage only applies in the latter case.