From the Super Mario Wiki, the Mario encyclopedia
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Mario Party series
Mario Party 6
Black holes make their first general appearance in the franchise in the Mario Party 6 duel minigame Black Hole Boogie. Here, both players must rapidly press to escape them. Also, in the minigame Seer Terror, one of the fortunes has Bowser sucked into a black hole.
Mario Party 8
Something similar to a black hole appears in Mario Party 8 in the background of the final boss minigame, Superstar Showdown. When Bowser is defeated, he gets sucked downwards into the vortex while stuck in his Koopa Clown Car.
Mario Party 9
Another black hole appears in Mario Party 9, in the background of the final boss minigame, Bowser's Block Battle. It seems to suck in large planets, as well as Mini Stars. When Bowser is defeated, he stumbles into the black hole, although in the final cutscene, it is shown that Bowser and Bowser Jr. can fly normally inside the black hole with their Koopa Clown Cars.
Super Mario series
Super Mario Galaxy
Black holes play a much larger role in Super Mario Galaxy, where they act as obstacles that suck in any characters, enemies and objects within its range. Most black holes are seen under floating landmasses, where they act as "pits", or else near areas with Sling Pods or cannons. If Mario or Luigi get too close to a black hole, its gravity begins to pull them in; being sucked into one instantly depletes the Health Meter, and they lose a life. Enemies destroyed by falling into black holes do not yield any coins or Star Bits.
In some galaxies such as the Hurry-Scurry Galaxy, successfully collecting a group of notes turns a nearby black hole into a Power Star. The Power Star pulls Mario or Luigi closer using a similar gravitational pull.
At the end of Super Mario Galaxy, after Mario has defeated Bowser for the final time, one of the planets near Bowser's gigantic sun undergoes a supernova and becomes a supermassive black hole, which quickly begins to engulf Mario, Princess Peach, Bowser and his entire fleet of Airships, Peach's Castle, and even the Comet Observatory. Just as everything is about to be destroyed, Luma suddenly appears in front of Mario, waves at him and then sacrifices himself by throwing himself into the black hole. Thousands of other Lumas soon join him in flinging themselves into the supermassive black hole in hopes of stabilizing it and ultimately saving the universe from destruction. Eventually, the black hole twists wildly around in space before finally exploding, thereby reforming the entire cosmos and creating an entirely new galaxy, which Mario welcomes in the final cutscene of the game.
Super Mario Galaxy 2
Black holes reappear in Super Mario Galaxy 2, serving a similar role. A black hole also features once more in the final battle against Bowser in Bowser's Galaxy Generator: defeating him in the first phase of the battle causes him to sucked into a black hole. He then emerges from the vortex, inhaling the final Grand Star and growing to a massive size to start the second phase. Defeating Bowser in this phase causes him to be sucked into a slightly larger black hole, which then sucks up the surroundings as well; Princess Peach and the final Grand Star are shot out of its remains several seconds later.
Mario & Sonic at the Olympic Winter Games
In the Wii version of Mario & Sonic at the Olympic Winter Games, a single black hole appears under the landing area in the Individual version of Dream Ski Jumping. If the player falls into it due to missing the landing area or falling off the edge of it, they will not gain any bonus points at the end of the event.