There are many mutations that can change the eye colour of a budgie, such as INO, Recessive Pied, Cinnamon, Fallow, Faded and Brownwing, however most of these are rare or only make the eye appear different for a few days after the chick hatches.
This is what most budgies have at maturity, black eyes with white iris rings.
This is the eye of a mature Recessive Pied, which should be solid black.
The eye of a mature INO (Albino or Lutino) should be red. The iris ring can range from white to pale pink, or can be slightly brown, depending on the bird.