Breadfruit
Its seeds, leaves, and blossoms are all edible. It's a starch of South Pacific Islanders and eaten much like a potato.
Carambola
Carambolas are considered a luxury item in supermarkets, and are also known as Starfruit, Carambas, Five Fingers, and Five Corners.
Cherimoya
Its ambrosia-like taste resembles that of a pineapple, banana, papaya, coconut, and mango all in one.
Currant
Currant berries are used to make jellies, pies, pudding, and sauces.
Guava
When making guava puree, include the rind; when combined with the pulp it has up to five times more Vitamin C than an orange.
Kumquat
Used most commonly in making syrups and preserves. They also taste great candied.
Lychee
The first book ever written on fruit in 1056 was about lychees. The National Cancer Institute is reportedly testing lychee roots for tumor fighting properties.
Passion Fruit
Commonly used for making passion fruit juice; its vine adorns many Hawaiian home gardens.