With the newest releases, I felt like I should update on which types are still not used in the games. This will fall into different categories:

1) Not used at all: this combo simply doesn't exist yet.

2) Legendary/Mythic Only: the type exists, but only for legendary or mythic pokémon. "Regular" ones don't have it yet.

3) Mega/Alternate Evolution Only: it is, effectively, a form change that doesn't last and no "regular" pokémon has it yet.

4) Regional Form Only: A regional variant of the pokémon (or its alt form) has this type combo, but there's not a new pokémon with it yet.

5) Reverse type: Flying and Fairy tend to be secondary types with only a handful or so of pokémon who have it as a primary type.

Note: 2, 3, and 4 are going to have some overlap. I'll list them.

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1
Normal/Ice
Normal/Bug
Normal/Rock
Normal/Steel

Fairy/Fire
Fairy/Ground

Ice/Poison
Bug/Dragon
Rock/Ghost

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2
Psychic/Dragon: Latios and Latias
Fire/Steel: Heatran
Rock/Fighting: Terrakion
Fire/Water: Volcanion
Psychic/Ghost: Hoopa, Lunala

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3
Dragon/Fairy: Mega Altaria
Psychic/Dragon: Mega Latios and Mega Latias
Electric/Fire: Heat Rotom
Electric/Grass: Mow Rotom
Psychic/Dragon: Ultra Necrozma
Psychic/Ghost: Dawn Wings Necrozma, Shadow Rider Calyrex

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4
Alolan
Electric/Psychic: Raichu
Ice/Steel: Sandshrew, Sandslash
Ice/Fairy: Ninetails

Galarian
Poison/Fairy: Weezing
Ice/Fire: Darmanitan Zen Mode
Poison/Psychic: Slowbro, Slowking

Hisuian
Electric/Grass: Voltorb, Electrode
Normal/Ghost: Zorua, Zoroark

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5
[12] Flying/Normal, Flying/Grass, Flying/Fire, Flying/Electric, Flying/Ice, Flying/Psychic, Flying/Fairy, Flying/Bug,
Flying/Poison, Flying/Ground, Flying/Rock, Flying/Ghost

[11] Fairy/Normal, Fairy/Grass, Fairy/Water, Fairy/Electric, Fairy/Ice, Fairy/Dragon, Fairy/Dark, Fairy/Bug, Fairy/Poison, Fairy/Rock, Fairy/Ghost

[8] Ghost/Normal, Ghost/Water. Ghost/Electric. Ghost/Ice. Ghost/Psychic. Ghost/Bug. Ghost/Fighting, Ghost/Steel

[7] Fighting/Normal, Fighting/Grass, Fighting/Fairy, Fighting/Bug, Fighting/Poison, Fighting/Ground, Fighting/Rock
[7] Steel/Grass, Steel/Fire, Steel/Water, Steel/Electric, Steel/Ice, Steel/Dark, Steel/Bug

[6] Psychic/Water, Psychic/Electric, Psychic/Bug, Psychic/Poison, Psychic/Ground, Psychic/Rock

[5] Ground/Fire, Ground/Water, Ground/Ice, Ground/Bug, Ground/Poison
[5] Ice/Grass, Ice/Electric, Ice/Dragon, Ice/Dark, Ice/Fighting
[5] Poison/Fire, Poison/Electric, Poison/Rock, Poison/Ghost, Poison/Steel

[4] Dark/Water, Dark/Electric, Dark/Bug, Dark/Rock
[4] Dragon/Grass, Dragon/Poison, Dragon/Rock, Dragon/Steel
[4] Grass/Water, Grass/Electric, Grass/Bug, Grass/Rock
[4] Normal/Fire, Normal/Electric, Normal/Dark, Normal/Poison

[3] Fire/Grass, Fire/Electric, Fire/Ice

[2] Electric/Bug, Electric/Rock
[2] Water/Normal, Water/Fire

[1] Bug/Ice

[0] Rock* (Rock/Normal, Rock/Ghost | Normal/Rock, Ghost/Rock do not exist)

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For further info on unique pokémon types, check out this link.