Botanically, fruit is a part of a flowering plant which contains its seeds.
Acai berries (fruit of the acai palm - the freeze-dried powder is about 30% fat.
Oil palm fruit is also high in fat; "palm oil" is derived from the fruit. "Palm kernel" oil comes from the seed of the fruit.
Coconut - is technically a drupe, but the mesocarp/flesh is fibrous & dry, and high in fat rather than water (like that in a drupe such as a peach) Walnuts also belong to this category.
True nuts are botanically fruit (they are basically the composite of a seed & fruit - two in one) - that includes filberts/hazelnuts, brazil nuts
Peanuts can also be considered a simple dried fruit high in fat, since they are the end form of the legume fruit (concealed inside a pod/'geocarp')
The carrot plant also produces a 'fruit' - which is a 'schizocarp', a dry fruit developing into multiple carpels (ovules) - so the carrot seed is essentially a fruit.
Almonds & pecans by themselves are not fruit, but the seeds of a fruit (drupe), similarly to cashews (seed of the cashew apple), the fruit itself in this case isnt high fat. Cocoa nibs are also seeds of a fruit.
Well, and the Durian, olives, avocado, that have already been mentioned.
Almonds and pecans http://www.livestrong.com/article/368839-fatty-fruits-vegetables/
Apples - variation in sugar content? 6 Answers
Do you eat freeze dried fruit? 5 Answers
How much fruit do people eat? 19 Answers
Does sulfured fruit upset your stomach? 11 Answers