These are: Bug, Dragon, Electric, Fighting, Fire, Flying, Ghost, Grass, Ground, Ice, Normal, Poison, Psychic, Rock and Water. Some Pokémon are dual-Types, such as Beedrill which is both Grass and Poison.
Here is a table illustrating how, in battle, pitching any particular Type against one's opponent would in general be great, poor or bad.
Your Type | Great choice against | Poor choice against | Bad choice against |
Bug | Grass, Poison, Psychic | Fighting, Fire, Flying, Ghost | - |
Dragon | Dragon | - | - |
Electric | Flying, Water | Dragon, Electric, Grass | Ground |
Fighting | Ice, Normal, Rock | Bug, Flying, Poison, Psychic | - |
Fire | Bug, Grass, Ice | Dragon, Fire, Rock, Water | - |
Flying | Bug, Fighting, Grass | Electric, Rock | - |
Ghost | Ghost | - | Normal, Psychic |
Grass | Ground, Rock, Water | Bug, Dragon, Fire, Flying, Grass, Poison | - |
Ground | Electric, Fire, Poison, Rock | Bug, Grass | Flying |
Ice | Dragon, Flying, Grass, Ground | Ice, Water | - |
Normal | - | Rock | Ghost |
Poison | Bug, Grass | Ghost, Ground, Poison, Rock | - |
Psychic | Fighting, Poison | Psychic | - |
Rock | Bug, Fire, Flying, Ice | Fighting, Ground | - |
Water | Fire, Ground, Rock | Dragon, Grass, Water | - |