What cat breeds have brown eyes?

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Answer 1

None of them.  The only time you see brown eyes in a cat is when it's a kitten whose eyes are in the process of changing to their adult color.  All kittens are born with blue eyes so as they change to gold or copper they may appear to temporarily look brown.

Cat eyes can be blue, green, gold or copper and in varying lightness or darknesses of those colours.  Coat colour determines eye colour.

Cats that are "pointed" (Siamese, Ragdolls, some Ragamuffins) have blue eyes.  

White cats can have blue, green, gold, copper eyes or "odd eyes" (one blue eye and one green or gold eye - often seen in Turkish Van and Turkish Angoras, for example)

Cats of other colours have green gold or copper eyes.