Action
Since "LittleBigPlanet" is mainly set up as a platformer adventure game, consisting of small characters running and jumping across different terrain in the environment, it makes the most sense that the action genre provides the largest array of options for level design. You can easily create pits and traps throughout a level, which can challenge players to jump and run at the correct time to avoid danger. Place enemies in the environment to oppose players; the behavior and movement speed of these adversaries allows for customization for an additional challenge. To immerse players further into the world of an action game, you can customize the avatar they control, Sackboy, with different costumes and colors. For example, color Sackboy in all black and give him a red headband, creating a ninja-like appaerance.
Racing
"LittleBigPlanet" also allows players to make vehicles to race through levels. Players can ride several different vehicles with multiple wheels, including carts, skateboards and trains. Add a switch to any one of these vehicles to give the player control over its speed. Deploy hills and other obstacles so players have to drive their vehicles carefully, avoiding a crash. Airborne vehicles are also a possibility, with jet packs allowing for quick bursts of speed or even a custom-made airship or hot-air balloon that uses thrusters to glide its way slowly through a level.
Puzzle
You don't have to design all levels in "LittleBigPlanet" around speed or confrontation. Levels can require players to think a bit when navigating. For example, you could make an insurmountable door or elevator that requires a certain artifact to access. The player would then have to scavenge the environment to find the artifact. Also, you can create switch puzzles, which require players to match up certain symbols, complete basic arithmetic or even listen to specific sounds.
Cooperative
You can also design a level around multiple players cooperating to advance. "LittleBigPlanet" allows you to set markers and checkpoints, which you can customize to require all players to reach them to proceed. In this way, you can design puzzles that require players to navigate a complicated maze --- with a jet pack, for instance --- or scale a hill collaboratively by placing blocks so each player can advance. When riding vehicles, one player can control the throttle and the other players could potentially be grabbing collectibles --- or just hanging on for dear life.