By Leveling Up:
* Tackle: Normal-type physical move
* Growl: Normal-type status move that lowers the opponent's Attack
* Tail Whip: Normal-type status move that lowers the opponent's Defense
* Quick Attack: Normal-type physical move with priority
* Fake Out: Normal-type physical move with priority that flinches the opponent
* Double-Edge: Normal-type physical move that also damages the user
* Take Down: Normal-type physical move that also damages the user
* Body Slam: Normal-type physical move that has a chance of paralyzing the opponent
* Play Rough: Fairy-type physical move that has a chance of lowering the opponent's Attack
* Swift: Normal-type special move that hits all opponents regardless of their ability
* Last Resort: Normal-type physical move that only works if all other moves have been used
* Helping Hand: Normal-type status move that increases the power of the next move used by an ally
* Return: Normal-type physical move that is more powerful if the user has high friendship
* Frustration: Normal-type physical move that is more powerful if the user has low friendship
* U-turn: Bug-type physical move that lets the user switch out after hitting the opponent
* Facade: Normal-type physical move that is more powerful if the user is poisoned, burned, or paralyzed
* Sucker Punch: Dark-type physical move with priority that only works if the opponent is about to attack
* Payback: Dark-type physical move with priority that only works if the opponent attacked before
* Night Slash: Dark-type physical move with a high critical hit ratio
* Shadow Claw: Ghost-type physical move with a high critical hit ratio
* Will-O-Wisp: Fire-type status move that burns the opponent
* Thunder Wave: Electric-type status move that paralyzes the opponent
* Toxic: Poison-type status move that poisons the opponent and gradually damages them over time
* Protect: Normal-type status move that protects the user from attacks
* Detect: Fighting-type status move that protects the user from attacks and reveals the opponent's move
* Endure: Normal-type status move that allows the user to survive with 1 HP
* Substitute: Normal-type status move that creates a substitute of the user's health
By TM/HM:
* Thunderbolt: Electric-type special move
* Thunder: Electric-type special move that has a chance of paralyzing the opponent
* Ice Beam: Ice-type special move
* Blizzard: Ice-type special move that has a chance of freezing the opponent
* Flamethrower: Fire-type special move
* Fire Blast: Fire-type special move that has a chance of burning the opponent
* Water Gun: Water-type special move
* Hydro Pump: Water-type special move
* Surf: Water-type special move
* Aerial Ace: Flying-type physical move that ignores the opponent's evasion
* Drill Peck: Flying-type physical move
* Brave Bird: Flying-type physical move that also damages the user
* Earth Power: Ground-type special move
* Earthquake: Ground-type physical move
* Mud-Slap: Ground-type special move that has a chance of lowering the opponent's accuracy
* Rock Slide: Rock-type physical move that has a chance of flinching the opponent
* Rock Tomb: Rock-type physical move
* Stone Edge: Rock-type physical move with a high critical hit ratio
* Ancient Power: Rock-type special move that has a chance of raising the user's Special Attack, Special Defense, Attack, and Defense
* Hidden Power: Normal-type special move that has different types depending on the Pokémon's individual values
* Cross Chop: Fighting-type physical move
* Low Kick: Fighting-type physical move that is more powerful against heavier opponents
* Brick Break: Fighting-type physical move that ignores the opponent's Defense stat
* Close Combat: Fighting-type physical move that lowers the user's Special Defense and Defense
* Focus Blast: Fighting-type special move that has a chance of lowering the opponent's Special Defense
* Shadow Ball: Ghost-type special move
* Psychic: Psychic-type special move
* Psybeam: Psychic-type special move that has a chance of lowering the opponent's Special Defense
* Future Sight: Psychic-type special move that hits two turns after it is used
* Dazzling Gleam: Fairy-type special move
* Moonblast: Fairy-type special move that has a chance of lowering the opponent's Special Attack
* Draining Kiss: Fairy-type special move that heals the user for half the damage dealt
* Light Screen: Psychic-type status move that reduces the power of special attacks for five turns
* Reflect: Psychic-type status move that reduces the power of physical attacks for five turns
* Amnesia: Psychic-type status move that raises the user's Special Defense
* Calm Mind: Psychic-type status move that raises the user's Special Attack and Special Defense
* Will-O-Wisp: Fire-type status move that burns the opponent
* Thunder Wave: Electric-type status move that paralyzes the opponent
* Toxic: Poison-type status move that poisons the opponent and gradually damages them over time
* Protect: Normal-type status move that protects the user from attacks
* Detect: Fighting-type status move that protects the user from attacks and reveals the opponent's move
* Endure: Normal-type status move that allows the user to survive with 1 HP
* Substitute: Normal-type status move that creates a substitute of the user's health
* Soft-Boiled: Normal-type status move that heals the user
* Synthesis: Grass-type status move that heals the user based on the amount of sunlight
* Roar: Normal-type status move that forces the opponent to switch out
* Whirlwind: Normal-type status move that forces the opponent to switch out
* Bulk Up: Fighting-type status move that raises the user's Attack and Defense
* Swagger: Normal-type status move that raises the opponent's Attack and confuses it
* Attract: Normal-type status move that makes the opposite gender attracted to the user
* Thief: Dark-type physical move that steals an item from the opponent
* Covet: Normal-type physical move that steals an item from the opponent
* Snatch: Dark-type status move that steals the effect of the opponent's move if it is beneficial
* Fake Tears: Dark-type status move that lowers the opponent's Attack and Defense
* Nasty Plot: Dark-type status move that raises the user's Special Attack
* Pain Split: Normal-type status move that makes the user and the opponent have the same HP
* Power Gem: Rock-type special move
* Rock Polish: Rock-type status move that raises the user's Speed
* Extreme Speed: Normal-type physical move with priority that ignores the opponent's evasion
* Last Resort: Normal-type physical move that only works if all other moves have been used
* Helping Hand: Normal-type status move that increases the power of the next move used by an ally
* Return: Normal-type physical move that is more powerful if the user has high friendship
* Frustration: Normal-type physical move that is more powerful if the user has low friendship
* U-turn: Bug-type physical move that lets the user switch out after hitting the opponent
* Facade: Normal-type physical move that is more powerful if the user is poisoned, burned, or paralyzed
* Sucker Punch: Dark-type physical move with priority that only works if the opponent is about to attack
* Payback: Dark-type physical move with priority that only works if the opponent attacked before
* Night Slash: Dark-type physical move with a high critical hit ratio
* Shadow Claw: Ghost-type physical move with a high critical hit ratio
* Quick Guard: Fighting-type status move that protects the user from priority moves
* Wide Guard: Rock-type status move that protects the user and its allies from moves that hit multiple targets
* Magic Coat: Psychic-type status move that reflects status moves back to the opponent
* Spikes: Ground-type status move that damages opponents that switch in
* Toxic Spikes: Poison-type status move that poisons opponents that switch in
* Stealth Rock: Rock-type status move that damages opponents that switch in
* Defog: Flying-type status move that removes hazards from the field
* Trick Room: Psychic-type status move that reverses the speed order of all Pokémon for five turns
* Will-O-Wisp: Fire-type status move that burns the opponent
* Thunder Wave: Electric-type status move that paralyzes the opponent
* Toxic: Poison-type status move that poisons the opponent and gradually damages them over time
* Protect: Normal-type status move that protects the user from attacks
* Detect: Fighting-type status move that protects the user from attacks and reveals the opponent's move
* Endure: Normal-type status move that allows the user to survive with 1 HP
* Substitute: Normal-type status move that creates a substitute of the user's health
* Memento: Dark-type status move that lowers the user's Attack and Speed and confuses the opponent before fainting
By Breeding:
* Charm: Fairy-type status move that lowers the opponent's Attack
* Fake Out: Normal-type physical move with priority that flinches the opponent
* Sweet Kiss: Fairy-type status move that has a chance of paralyzing the opponent
* Covet: Normal-type physical move that steals an item from the opponent
* Baby-Doll Eyes: Fairy-type status move that lowers the opponent's Attack
* Tickle: Normal-type status move that lowers the opponent's Defense and Attack
* Disarming Voice: Fairy-type special move
* Fairy Wind: Fairy-type special move
* Mystical Fire: Fairy-type special move that has a chance of lowering the opponent's Special Attack
This is not an exhaustive list, as some moves may also be learned by other means, such as breeding or events.