This concept applies to games in which the player is given direct control over a spherical object or living thing that rolls across surfaces. The sphere may either move independently, or be rolled by a separate character (like The Prince in Katamari Damacy), but - the ball must always move as if it were moving by itself. If the player character has to move around to different sides of the ball to push it in different directions, for instance, it would not be an example of the concept. Pinball games, or any other situation in which the ball is being moved with other objects, are also not included.
The classic arcade puzzle game Marble Madness is the archetype of an entirely rolling-based game, and inspired many imitators with its abstract style.
Perhaps the best-known example of this concept overall is Samus Aran's Morph Ball ability in the Metroid franchise, which allows her to curl up into a sphere and roll about. In Metroid Prime Pinball, Samus is usually in Morph Ball form, but since the player has no direct control over the Morph Ball (only the flippers), the game is not an example of this concept.