One of the most healthful but worst smelling fruits (at least when fully ripe or overripe) belongs to the Noni or Indian Mulberry (Morinda citrifolia). This now naturalized plant was brought here to the Hawaiian Islands by the ancient Polynesians, and they made very good use of it. Red dye was made from the bark and yellow dye was made from the roots. Although not very tasty, Noni fruit is edible and can be consumed as a nutritious famine food. Juice from the fruit was used for a variety medicinal purposes, and it is still quite popular for this today. It's not only humans that appreciate Noni, the fruits are also popular with birds like this Japanese White-eye or Mejiro (Zosterops japonicus).
Noni is an evergreen shrub or small tree in the Madder Family (Rubiaceae), and despite its common name of Indian Mulberry, it's not actually a true mulberry. It has large, shiny, up to 1 foot (30 cm) long leaves and white, 5-lobed flowers.
The flowers are followed by green fruits that gradually become yellow, and then turn dull creamy white when fully ripe and ready to fall from the tree.
Not only do the ripe and overly ripe fruits look rather disgusting with their soft, bulging, white-translucent, beetle grub-like flesh covered with sucker-like markings, they also smell quite disgusting. If you cut open one of these soft, white fruits, you'll be greeted with their stomach churning odor of vomit mixed with a hint of garbage ooze.
The unripe green fruits are hard and have an pungent green smell, while the much more appetizing semi-ripe yellow-white ones are firm and smell like fresh lettuce and taste rather like celery. Smell may not always be an indicator of taste, but the yellow-white fruits do seem to be the most palatable. However, I don't know what the bad-smelling green or white fruits taste like since I just haven't been brave enough to try them.