From the Super Mario Wiki, the Mario encyclopedia
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Koopa balls (generically referred to by Nintendo Power as magical balls) are balls with star patterns on them that Lemmy Koopa can shoot from his magic wand. They are usually small, but can come in large varieties as well. Although they are usually found in fights with Lemmy, sometimes they appear as obstacles in his castles.
Super Mario series
Super Mario Bros. 3
Koopa balls are first seen in Super Mario Bros. 3, where Lemmy attempts to shoot them at Mario while balancing on one himself. They bounce on the floor, changing direction when they bump into a wall. If Mario touches one, he takes damage, unlike in future games; however, jumping on one merely bounces him upwards.
New Super Mario Bros. Wii
Koopa balls once again return in New Super Mario Bros. Wii, but instead of hurting Mario if they touch him, as in Super Mario Bros. 3, they instead simply bump him, which can push him off the edge. Koopa balls also changed colors from green with orange stars to yellow with orange stars. Koopa balls appear in World 3-Tower and World 3-Castle, where Lemmy himself is fought. Mario is supposed to jump off of the balls to reach Lemmy, due to the icy floor. In the Castle fight, Lemmy has Kamek enlarge his ball, so he can bounce on it to move around. The balls also appear in the World 3-Castle level itself, bouncing above spikes leading to the Star Coin.
New Super Mario Bros. 2
New Super Mario Bros. U / New Super Mario Bros. U Deluxe
Super Mario Maker 2
In Super Mario Maker 2 versions 3.0.0 and later, Lemmy balances on top of a Koopa ball while shooting more out of his wand.
Puzzle & Dragons: Super Mario Bros. Edition
Lemmy is seen riding a Koopa ball in his fights in World 2-Castle and World 2-Airship.
Mario & Luigi: Paper Jam
Lemmy rides a giant Koopa ball in one of his attacks in Neo Bowser Castle, when fighting alongside Morton Koopa Jr. and Iggy Koopa. Lemmy rides his ball to try and crush Mario and Luigi, but fails if he is hit by the boomerang.
Paper Mario: Color Splash