Here is a list of all the type combinations which fit your criteria:
Type combinations based on Normal:
- Normal/Poison
- Normal/Flying
- Normal/Psychic
- Normal/Bug
- Normal/Ghost
- Normal/Fairy
Type combinations based on Fire:
Type combinations based on Water:
Type combinations based on Electric:
- Electric/Grass
- Electric/Flying
- Electric/Bug
Type combinations based on Grass:
Type combinations based on Ice:
- Did you expect any to be here? Nope. None. :(
Type combinations based on Fighting:
Type combinations based on Poison:
Type combinations based on Ground:
Type combinations based on Flying:
Type combinations based on Psychic:
- None here, but Psychic/Steel does before Gen 6. :(
Type combinations based on Bug:
Type combinations based on Rock:
Type combinations based on Ghost:
- Ghost/Dark
- Ghost/Steel, before Gen 6
Type combinations based on Dragon:
Type combinations based on Dark:
- Dark/Poison
- Dark/Ghost, before Gen 6 and the Fairy type.
Type combinations based on Steel:
Type combinations based on Fairy:
So there you have it. Hope I helped.
Source: The Dual Type chart