I agree with those who mentioned Steel/Fairy, while its only weaknesses are rather common attacking types (Ground and Fire) it still has loads of resistances and two immunities (Dragon and Poison). Other notable ones include Water/Ground (only weak to Grass, and most of this combination's members tend to be bulky as well), Ghost/Dark (it may now be weak to Fairy, but it's still got minimal weaknesses due to the scarcity in numbers of Fairy Pokemon), Fire/Dragon (good offensive coverage, and only resisted by a select few type combinations), and Steel/Ghost (again has good neutral offensive coverage, and has a fair share of resistances and immunities as well).
As for type combinations that haven't existed yet, some really impressive ones would be Ghost/Fairy (again this combination has good neutral offensive coverage, plus has three immunities and only two weaknesses) and also Normal/Ghost (three immunities and is only weak to Dark). Definitely want those pulled off in future generations.