Moves that change the user's type:
Camoflauge
Changes the user's type, depending on where you use it.
In a building, or WiFi battling: Normal
A cave or near a mountain: Rock
In a field, grass or a swamp: Grass
In a desert or road: Ground
In water: Water
In snow: Ice
Conversion
Changes your type to the type of one of your moves. It is random, however. You will recieve STAB from the type of the move you copied (so there will always be a STAB move after you use it).
Conversion 2
Changes your type so you are resistant to the type of the move your opponent last used. Will fail if you are already that type.
Reflect Type
You get the exact same typing as your opponent. If they are dual-typed, you become dual-typed as well.
Moves that change the opponent's type:
Soak
Changes the opponent's Pokémon to the Water type. They lose their previous types, STABs, resistances, weaknesses and immunities.
Forest's Curse
The opponent's Pokémon gains the Grass type. So, single-typed Pokémon become dual-typed and dual-types become tri-typed. It will fail if the opponent is already Grass typed.
Trick or Treat
Exactly like Forest's Curse, but with the Ghost type instead.
Plasma Fists: Turns all Normal Type moves to Electric during that turn.
Abilities that change your type:
Colour Change
Changes your type to the type of the last move you were hit with whenever you get hit by a move.
Protean
Changes your move to the type of the move you are about the use whenever you use a move. You will always get STAB.
Aerilate:
Normal type moves will become flying type.
Normalize
All your moves become normal type.
Pixilate
Normal type moves become fairy type.
Refrigerate
Normal type moves become ice type.
Multitype
Changes forme and type based on what plate it is holding.
Normal: No plate
Fire: Flame plate
Water: Splash plate
Grass: Meadow plate
Electric: Zap plate
Ghost: Spooky plate
Steel: Iron plate
Dark: Dread plate
Fairy: Pixie plate
Dragon: Draco plate
Bug: Insect plate
Fighting: Fist plate
Ice: Icicle plate
Flying: Sky plate
Ground: Earth plate
Rock: Stone plate
Psychic: Mind plate
RKS System
Works the exact same as multitype
Moves that change a move's type:
Electrify
If you hit the opponent right before they use their move (so hitting first on that turn), their move will become electric type.
Ion Deluge
Targets the whole field, all normal type moves become electric type.
Weather Ball
Changes type based on the weather. Becomes 2x as powerful when there is weather.
None: Normal
Sunny: Fire
Hailing: Ice
Raining: Snow
Sandstorm-ing: Rock
Judgment
Changes type just like multitype.