The ability to teleport allows an entity to move to a nonadjacent location, skipping over locations in between. While this is most often used by agents with the goal of reaching another location, it can also be used by entities without goals. Teleportation is not often used as a game goal as it offers no challenge to the player. Instead, when it's based on the decision of an entity, it is used as a benefit to the entity allowing it to avoid potentially dangerous locations in between its current location and its location goal. It can also be used to create distance more quickly between the agent and a potentially dangerous entity. While an entity may be able to reach its final destination by teleporting, games do not allow player-controlled entities to teleport from their starting location to the location goal as it also offers no challenge to the player.
In Diablo II, the player-controlled sorceress can have the ability to teleport from one location to another. This allows her to escape situations where she is surrounded by enemies, or to move quickly to locations to which traversing would require a longer route.
In Mega Man (all versions, aside from Zero series), the player chooses a level in which to play from a stage selection screen. The Mega Man avatar then teleports from a (supposed) base of operations to the selected level. Upon completing the level, the avatar then teleports back to the stage selection screen. Such teleportation is necessary for completion of game goals and indirectly controlled by the player's actions.
This is a weak example because the teleportation is representational (ie, the player sees a visual enactment of teleportation) and also because it transcends different levels. It is also arguable that the stage selection screen is actually a playable location, serving more as a menu from which destinations are chosen.
In Legend of Zelda (many versions), the player has the option to teleport to the entrance of a dungeon if they are hopelessly lost or do not wish to traverse a completed (non-challenging) dungeon. This ability is not required to accomplish game goals. In Legend of Zelda: A Link to the Past specifically, the player acquires an item (the magic mirror) which allows him to "teleport" to and from the Dark World, a second area in the game which must be traversed in order to accomplish the game's goals normally (game code exploits are ignored here). The teleportation in this case is somewhat of a non-standard movement "in" and "out" of the Dark World because Link's position in the destination world is related to his position in the source world, since the movement is a "dimensional teleport."
In Super Mario Brothers, the player-controlled entity "teleports" from one place in a level to another by going down a green pipe. This is a weak example because the entity moves through a seperate space (usually a room) in order to teleport. The teleportation does not happen instantaneously. However, this movement does move the player-controlled entity to a nonadjacent location.