They are bred to not fruit with with varying degrees of success, it is not common to occasionally get some kind of fruit. My 30-year old purple leaf plum gives a few fruits every year and my 30-year old weeping cherry fruits every few years. The cherries are very bitter on my tree.

Scott

Actually, most cherry trees, that are produced for flowers vice fruit, also produce very small cherries. The cardinal birds love them. Sometimes the fruits are extremely small and not obvious to the casual observer. If you want to grow cherries on your flowering cherry tree, you can graft a fruiting cherry limb on the tree and have both flowers and cherries.

Ornamental plum trees here in Portland occasionally produce a few golf-ball-sized fruits, some quite sweet.

Japanese ornamental cherries may occasionally fruit, in some situations.

I have gotten the opportunity to taste one of these fruits when they are fully ripe. When fully ripe they are very dark and have a very dark scarlet juice that stains. The fruits can be pretty juicy, but the fruits are pretty small and don't have much edible flesh, a very small flesh to seed ratio. The taste has a lot of bitterness and are not very sweet. The first thing that hits you is the bitterness, but after that there's an aftertaste of intense cherry cough syrup, which is a little stronger tasting than regular sweet cherries. It almost makes me think these could be used for culinary flavoring, but you'd have to want bitterness too (like in certain alcoholic cocktail drinks). Might not be a good idea to eat too many though.

The most common Japanese ornamental cherry variety, Yoshino, is a very poor pollinator, so usually cannot pollinate itself, which means no cherries. Kwanzan is a sterile variety, cannot produce fruit, and the others require a different cherry variety (any species) to pollinate it if any fruit is to form.