Pokémon Type Chart

http://i.imgur.com/c1z5YTa.png

    New types:
Normal/Dragon    - Drampa
Electric/Psychic - Raichu (Alola form)
Ice/Steel        - Sandslash (Alola form)
Ice/Fairy        - Ninetales (Alola form)
Fighting/Ice     - Crabominable
Fighting/Ghost   - Marshadow
Poison/Fire      - Salazzle
Bug/Fairy        - Ribombee
Rock/Electric    - Golem (Alola form)
Rock/Poison      - Nihilego
Ghost/Fairy      - Mimikyu
Dragon/Fighting  - Kommo-o
Dark/Normal      - Raticate (Alola form)

    Remaining types:
Normal/Ice
Normal/Poison
Normal/Rock
Normal/Ghost
Normal/Steel
Fire/Ice
Fire/Fairy
Electric/Fighting
Electric/Poison
Electric/Dark
Grass/Fire
Ice/Poison
Fighting/Fairy
Poison/Fairy
Ground/Fighting
Ground/Fairy
Psychic/Poison
Bug/Normal
Bug/Ice
Bug/Psychic
Bug/Dragon
Bug/Dark
Rock/Ghost
Steel/Poison
Dark/Fairy

    Remaining types (expanded):
Normal   - Ice, Poison, Bug, Rock, Ghost, Steel         {6}
Poison   - Normal, Electric, Ice, Psychic, Steel, Fairy {6}
Bug      - Normal, Ice, Psychic, Dragon, Dark           {5}
Fairy    - Fire, Fighting, Poison, Ground, Dark         {5}
Ice      - Normal, Fire, Poison, Bug                    {4}
Fire     - Grass, Ice, Fairy                            {3}
Electric - Fighting, Poison, Dark                       {3}
Fighting - Electric, Ground, Fairy                      {3}
Dark     - Electric, Bug, Fairy                         {3}
Ground   - Fighting, Fairy                              {2}
Psychic  - Poison, Bug                                  {2}
Rock     - Normal, Ghost                                {2}
Ghost    - Normal, Rock                                 {2}
Steel    - Normal, Poison                               {2}
Grass    - Fire                                         {1}
Dragon   - Bug                                          {1}
Water    - COMPLETE                                     {0}
Flying   - COMPLETE                                     {0}

Both Grass and Dragon only need one more combination to be finished: Grass/Fire and Dragon/Bug
Besides Water, Flying, Grass, and Dragon, every type is missing a Normal, Poison, and/or Fairy combination.
Fun fact: The Pokéstar Studios opponent "F-00" is Steel/Normal but is not a Pokemon. http://bulbapedia.bulbagarden.net/wiki/Pokestar_Studios_opponents#F-00