If you remember the instruction booklet for the original Super Mario Bros., you may recall that the Koopa tribe was “famous for their black magic,” and Bowser identified as a “sorcerer king.” Not that any of the Koopas really used magic within the game, unless you count the endless hammers from nowhere that the King and the Hammer Bros. were able to produce.
The instruction book specifies that they turned the Mushroom People “into mere stones, bricks and even field horse-hair plants.” This idea occasionally came up in the Super Mario Bros. Super Show cartoons, as in “The Ten Koopmandments” when King Koopa transformed Toads into bricks to make a sphinx, and “Flatbush Koopa” when he did much the same to New York City policemen. He used a magic staff in the former and a wand-like scepter in the latter. Super Mario Bros. 3 has the seven Koopalings steal the magic wands from seven kings and turn them into animals.
Again, this is reflected in the cartoon version, although it’s not always specified whether the wands they use are their own or stolen.
In one episode, Toad gets his hands on a wand made for the Wizard King of the West and uses it to make chairs dance and pipe creatures come to life. The Koopalings then take it and increase the size of a fence and a Nipper Plant. Another episode involves Bowser using a wand to turn some of his kids into giant ninjas.
And in one of the Nintendo Adventure Books, Koopa Capers, Wendy O. Koopa finds a spell to combine the power of seven wands into one. When playable in Super Mario RPG, most of Bowser’s attacks involve summoning monsters to help him out, but he can also make a column of earth emerge from the ground.
The original Mario anime makes him a shape-shifter, an ability he occasionally has in the games as well.
He’s also been known to summon lightning and teleport.
Super Mario World is the first game to introduce Magikoopas, who dress and act somewhat like Wizzrobes from the Zelda series.
They can appear and disappear at will, and transform blocks into Koopa Troopas. In some later games, they can summon other monsters, perform other magic-based attacks, and turn themselves into energy for fast travel. The most powerful Magikoopa, who also appears to have done much of the work in raising Bowser, is Kamek.
In addition to the usual Magikoopa powers, he is capable of divination and psychokinesis, and has mechanical skills as well. His introduction in Yoshi’s Island has him riding a broomstick and making monsters grow, much in the same fashion as Rita Repulsa from Power Rangers. In Super Mario RPG, a Magikoopa who is probably Kamek heals your party and creates a block that produces unlimited money.
If Bowser has an adviser who can do that, why is he always stealing things? Maybe it’s only a limited-time spell. Later games often have him helping out Bowser and his kids in their battles against Mario and Luigi.