Are there any types which do not appear on a single-type Pokémon?

Question

Before Black/White, all Flying type Pokémon were dual-type (e.g. Normal/Flying, Fire/Flying). Thundurus is the first pure Flying type.

Are there any types left of which there are no pure-typed Pokémon?

Answer 1

Flying was the only holdout with no pure type pokemon, which as you note Gen V changes. From Bulbapedia:

Prior to Generation V, this type was the only one of the seventeen that was never seen as an authentic pure type; Tornadus is the first pure Flying type.

There are, however, a large number of type combinations that don't exist.