By leveling up:
* Scratch: A basic, physical move that deals damage.
* Growl: A status move that lowers the opponent's Attack stat.
* Tail Whip: A status move that lowers the opponent's Defense stat.
* Fake Out: A priority move that deals damage and forces the opponent to flinch.
* Quick Attack: A priority move that deals damage.
* Charm: A status move that lowers the opponent's Attack stat.
* Payback: A move that deals more damage if the opponent attacks first.
* Swift: A move that hits all opponents, ignoring accuracy.
* Double-Edge: A powerful move that also damages the user.
* Last Resort: A move that deals more damage if the user has used other moves.
By TM:
* Thunder Wave: A status move that paralyzes the opponent.
* Thunder: A powerful Electric-type move that has a chance to paralyze the opponent.
* Ice Beam: A powerful Ice-type move that has a chance to freeze the opponent.
* Flamethrower: A powerful Fire-type move that has a chance to burn the opponent.
* Shadow Ball: A powerful Ghost-type move.
* Energy Ball: A powerful Grass-type move.
* Return: A powerful move that deals more damage based on the user's affection.
* Frustration: A powerful move that deals more damage based on the user's unhappiness.
By breeding:
* Covet: A move that steals an item from the opponent.
* Baby-Doll Eyes: A status move that lowers the opponent's Attack stat.
* Attract: A status move that makes the opponent infatuated with the user.
* Sing: A status move that puts the opponent to sleep.
* Will-O-Wisp: A status move that burns the opponent.
* Uproar: A move that deals damage and prevents the opponent from switching out for two turns.
By tutoring:
* Quick Guard: A move that protects the user and its allies from priority moves.
* Endure: A move that allows the user to survive a single attack with 1 HP remaining.
* Tickle: A move that lowers the opponent's Defense and Attack stat.
By other means:
* Hidden Power: A move whose type and power depend on Skitty's individual values.
* Natural Gift: A move whose type and power depend on the held item.
This is not an exhaustive list, as Skitty can also learn other moves through various methods, such as event-exclusive moves, or by using certain held items.
It's important to note that some of these moves might not be available in every generation of Pokémon games, and some moves might be restricted based on the specific game version.