What fruits will naturally ferment?
First, before talking about fruits, let's remember that fermentation is an energetic metabolic process where there is no net oxidation of the substract. Bacteria, fungi, animals like you and me and even plants can use fermentation in different occasions. Plant cells, like fungal cells (and unlike bacteria and animal cells) perform alcoholic fermentation. So, there is no need of a fungal contamination to make a plant tissue producing ethanol.

But, of course, the presence of fermenting fungi, particularly yeasts, can make alcoholic fermentation much faster and noticeable. Several fruits contain what is called "ambient yeasts" (differing from "cultured yeasts", which we add to the fruits latter) covering them, and I believe the most famous example are grapes. Grapes are covered by several genera of Ascomycota (like Candida and Pichia), which can lead to alcoholic fermentation of the fruit. These species are different from Saccharomyces cerevisiae, the most common "cultured yeast" (and the one used in winemaking), but they can produce ethanol the same way. 

This "natural fermentation" of grapes is known for a very long time, and it's probably one of the first cases of natural alcoholic fermentation known by civilized man.

EDIT: references for alcoholic fermentation in plant cells:


http://www.plantphysiol.org/content/149/2/1087.full



  Under oxygen-limiting conditions, pyruvate can either be converted into ethanol by pyruvate decarboxylase (PDC) and alcohol dehydrogenase (ADH) or to lactate by lactate dehydrogenase.



http://www.plantphysiol.org/content/100/1/1.full.pdf+html



  During the early hours of germination [...] seeds rapidly generate high respiratory quotients and exhibit increased ADH2 activities and active alcoholic fermentation.