Divination (占い) is the ability to see events far away in time and space, usually through Crystal Balls. Fortuneteller Baba and Old Kai (being the fusion of an Old Witch and a Supreme Kai) are known to use this power, with the former using it for money.
In the anime, the Water Jug Monster that lived inside the water jugs on Korin Tower possessed the ability to project the past, present, and future through water jugs.
Baba uses this ability several times in the series, mainly to help Goku when he happens to be in great need. She used this to help him find a sealed Dragon Ball, and later to find the lost Bansho Fan. Baba correctly predicted that Goku would save the world one day. She also used her art to project the Z Fighters' fight against the Saiyans, as well as Gohan's fight against Cell; while Baba's Crystal Ball shattered by the sheer amount of ki used in the former, the same did not happen in the latter saga, though it is reasonable to think that Baba simply acquired a stronger ball after the Saiyan conflict.
The Kanassan Toolo also uses this art, which he passes to Bardock via a secret Kanassan technique as a form of retribution for the misdeeds of Bardock and the Saiyans in general. Bardock would have visions of his planet's destruction in between time, with no control over this power.
In the anime during the Frieza Saga while SSJ Goku is still fighting Frieza on Dying Namek, Bulma tries to cheer everyone up by predicting Goku's fate with fortune telling leaves. She draws a circle in the ground and places three leaves inside it, planning to burn them. If they all burn, it means Goku will return safely. Dende sets fire to them, but the wind blows them away before they can burn completely. However the validity of this type of divination is questionable (as it occurs in anime Filler and appears to be noting more than a simple fortunetelling game based on little more than superstition) and even Gohan scoffs at it, confident that Goku will survive which later turns out to be more accurate than the game's prediction as Goku defeats Frieza and escapes Dying Namek using one of the Ginyu Force's Attack Balls.
The Oracle Fish is a fish which has prophetic powers. It appears in the movie Dragon Ball Z: Battle of Gods: 39 years ago, the Oracle Fish told the God of Destruction Beerus that a strong opponent would appear before him and during the events of the film, it helps Beerus to find Goku, the one who defeated Frieza.
Video Game Appearances
In Dragon Ball Z II: Gekishin Freeza, in "Exit the Universe" after Goku arrives on Planet Kanassa and defeats the Combatants stationed there freeing the surviving Kanassans from Frieza's rule, he is thanked by the Kanassans who knows about Bardock's sons through his divination ability.
In Dragon Ball Xenoverse, Bardock's ability to see the future is mentioned in the Legendary Super Saiyan Saga by Future Trunks who explains that it is due to this ability that Bardock is aware that Dark Broly must not be allowed to interfere with Super Saiyan Goku epic battle with Frieza on Dying Planet Namek. Bardock explains he is fully aware that his son Kakarrot will be the one to defeat Frieza and avenge the Saiyan race. It is also the reason he is aware that Prince Vegeta can preform the Power Ball technique, knowledge which he puts to good use when he encounters Vegeta on Earth while the Future Warrior is fighting Dark Broly.
In the Resurrection ‘F’ Pack DLC, Elder Kai (as the Future Warrior's current Master) will occasionally use his ability to tell the Warrior's fortune. The Warrior's chances of obtaining items & skills in Parallel Quest may increase depending on the vision he receives. If his vision is of a tree baring a Golden Fruit, then the item & skill drop rate greatly increased for the next Parallel Quest.
In Dragon Ball Xenoverse 2, Bardock's ability to see the future is shown twice in the opening prologue which shows a alternate version of Bardock's final battle during the Genocide of the Saiyans in Age 737. The first time occurs while he is fight some Frieza Force soldiers, which depicts him witnessing a vision of Goku confronting 1st Form Frieza on Namek like he did in the special.
After snapping out of it, Bardock defeats the soldiers and screams for Frieza to show himself. As 1st Form Frieza appears and Bardock demands he explain why he is attacking them, a new vision is of Age 779 is shown. In Bardock's new vision he sees Golden Frieza confronting his son Kakarot in his Super Saiyan Blue form watches the two clash which generates an explosion and the vision ends, causing Bardock to attack 1st Form Frieza with the Final Spirit Cannon only for it to be consumed by Frieza's Supernova leading to his and Planet Vegeta's destruction.