Quoted By:
Fire: Charizard
Electric: Pikachu
Ghost: Gengar
Normal: Snorlax or Meowth
Grass: Bulbasaur
Water: Blastoise, Greninja, or Squirtle
Flying: Charizard or Rayquaza, if I'm not allowed repeats then Lugia, Zubat, or maybe even Corviknight in a few years
Bug: Butterfree
Rock: Onix
Ground: Diglett, Cubone, Rhydon, Donphan, or Garchomp
Dark: Umbreon, Greninja, or Tyranitar
Steel: I don't think there are any super iconic steel types besides Lucario, which I think most people think of as a fighting type first.
Psychic: Mewtwo
Fighting: Lucario or Machamp
Ice: Lapras
Poison: Arbok, Weezing, Zubat. I'd include things like Gengar but I think they're more associated with their other type.
Dragon: Rayquaza
Fairy: Jigglypuff