Note: Not to be mistaken with the game itself taunting the player.
Taunts are found in all sorts of games often through a button or menu, but especially common in fighting games.
Designated taunts are usually risky to do and happen at the expense of performing more outwardly useful actions but largely with the goal to provoke.
This is similar but distinct from Tea-bagging as commonly seen in Halo multiplayer. The difference is that a taunt is a distinct action rather than repeating a safe action like crouching, though tea-bagging is just one example of other actions being able to provoke a response like taunts.
Real Time Games
The Street Fighter Alpha series both popularised the feature by having Dan Hibiki, the franchise's gag character being able to perform them in the air, on the ground and even as a Super Combo (Legendary Taunt) which exclusively wastes meter.
Dan did have the ability to do very limited damage with Harmful Taunts which were impractical even if unique, this extended to the Street Fighter IV games allowing him to cancel his 7 second long Legendary Taunt super into an Ultra Combo.
More practical taunts include like Luigi's Down Taunt in the Super Smash Bros. series which offers an exclusive kill option and the Street Fighter III games which also had stat adjustments assigned to them with Q's one lowering the damage taken during the round which made them especially valuable.
Super Smash Bros. Melee and its sequels introduced and continued the concept of "Smash Taunts" where performing quick taunt commands with specific characters on select stages would lead to conversations between NPCs and the character starting the taunt, often making comments on the opponent's character as well as sharing general advice.
There is a considerable risk in performing them as the one taunting is vulnerable for a brief moment and a Smash Taunt can be done once per match, but the payoff is a brief commentary featuring similar presentation to the games that the characters came from. Hence, Palutena's Guidance resembles the commentary in Kid Icarus: Uprising, Star Fox's Smash Taunts call back to banter in Star Fox 64 & following games and the Codec Conversations resemble Metal Gear Solid.
Even outside of fighting games and multiplayer versus, taunts have been implemented extensively by the Devil May Cry and Bayonetta series. The former used taunts to keep the Style Meter active which increased the score and earned orbs even if the taunt can't hurt foes while the latter implemented a rage mode for enemies when they get taunted.
Turn Based Games
Within turn based games like some RPGs, it is often possible to select a taunt skill to draw aggression to a specific member of your party if not increase the odds of the enemy doing certain actions in 1 versus 1 situations.