Petrification is the act of turning something to stone. It is a common trope of myth and fantasy; ancient Greek myth told of a woman named Medusa that was cursed with a hideous appearance; any that made eye contact with her would immediately be turned to stone. The act of petrification has also been often depicted in video games in one manner or another. The following are only a small subset of examples in how it has been used and depicted.
Fire Emblem: Radiant Dawn
At the end of the third part of Fire Emblem: Radiant Dawn's story, the goddess Ashera is awakened from her self-imposed slumber at a time when a major war has engulfed all of the nations and races of Tellius. Disgusted by this behavior, she follows through on the promise she made before she entered her long slumber and passes judgment on the people of Tellius by turning nearly everyone to stone. The only people that are able to resist are warriors of particular strength, and the Branded; beings born of beorc and laguz heritage.
Dragon Quest V: Hand of the Heavenly Bride
In Dragon Quest V, the hero's wife is kidnapped by monsters shortly after the celebration of the birth of their twins. When the hero arrives to rescue her, they are both turned to stone and remain as statues for eight years while their children grow up without them. The two are eventually freed from their curse and fight together to stop the lord of darkness from taking over the land.
Final Fantasy XIII
An example of non-stone petrification, the l'Cie of Final Fantasy XIII that manage to successfully complete the Focus assigned to them by a fal'Cie are transformed into crystal. Additionally, any l'Cie that fails to complete their Focus in time will transform into a monster known as a Cie'th, and the Cie'th will in turn eventually petrify. These Cie'th Stones carry memories of the unfortunate l'Cie that they once were. Players can engage in sidequests by examining Cie'th Stones and completing the Foci that were once assigned to them.
Elite Beat Agents
In the rhythm game Elite Beat Agents, the final challenge of the game is to overcome the Rhombulans, an alien race that hates music. In their conquest of Earth, they turn any people that sing and dance to stone. Their power also briefly affects the agents themselves, but they break free of their petrification and fight back by leading the entire world in a song-and-dance-based counterattack. However, if the player fails the final stage, the Rhombulans turn the entire population of Earth to stone.
Kid Icarus: Uprising
In Kid Icarus: Uprising, after Pit manages to free Palutena from the Chaos Kin's control, the Chaos Kin tears Palutena's soul from her body, causing her to turn to stone. She is restored to her former self after Pit and Dark Pit enter the chaos realm and manage to both stop the Chaos Kin and retrieve her soul.
There is also an item in the game called "Medusa's Head." A model of her head rather than her actual noggin, it appears in both single-player and multiplayer modes and functions like a turret. Once the player sets it, it will fire beams that temporarily petrify any target caught in its blast.
Super Mario Bros. 3
In Super Mario Bros. 3, one of the power-ups that Mario can acquire is the Tanooki Suit. The Tanooki Suit grants the same capability of flight as the Super Leaf. However, it also imparts the ability to temporarily turn into an invincible statue. Though the Tanooki Suit appears again in Super Mario 3D Land, it does not allow such a transformation until certain gameplay criteria are met.
Shin Megami Tensei: if...
During the course of Shin Megami Tensei: if..., two of the protagonist's classmates, Ryuuichi and Akiko, are turned to stone. If the player's path takes them through the Wrath dungeon, a demon will try to trick the protagonist and his/her partner into the belief that they can be restored by smashing the stone. If the protagonist doesn't fall for it, the partner will. As a result, Ryuuichi and Akiko are smashed to pieces, killing them both.