I couldn't find this on Google, so thought I'd throw this out there.

What type combinations haven't been done yet?

Also, for bonus points:

What type combinations only exist as Legendaries?
How would a new type combination be feasible?
Should an existing Pokemon be given a different type combination?

For that last one, look at Magnemite/Magneton, they were changed from Electric to Electric/Steel, which makes perfect sense.

Fire needs to be paired with more types, like Ice, Grass, Dragon or Water. Furthermore, there are no Bug/Fire Pokemon, there is only one Fire/Flying non-Legendary and the only Steel/Fire Pokemon is a Legendary. I think a Water/Fire Pokemon is completely feasible. Not sure about Ice/Fire, unless it was some kind of literally half-fire, half-ice Pokemon.

Also, obviously there has never been a pure-Flying type. Should there be? Just to shut people up about this fact?