The only type that is super-effective against Normal-type Pokemon is Fighting. Any other type normally effects it, except for Ghost. Ghost-type moves (other than moves that don't do damage) don't effect Normal-type Pokemon at all.
fire
Also flying
And if you are playing in the 1st Generation then poison is also effective.
dragon vs dragon dragon vs ice
Both Fighting types and Bug types are super effective against Dark types.
fighting types and bug types are the most effective types on dark.
ground type Pokemon are super effective against poison type Pokemon.
Psychic and flying types are super effective against fighting types.
normal type Pokemon are not super effective against any type.
fire is regularly effective against ghost types
dragon and ice is most efective against dragon.
Fire and fighting type moves are super effective against Ice type pokemon.
The most effective in rock type Pokemon is water Pokemon ofcourse.
Fire type Pokemon are super effective against bug types
psychic and flying Pokemon are good against fighting type-pokemon
Fighting and Bug types are super effective.