Yes, it is possible to produce a tree that doesn't require pruning, but the only one that I know of isn't really a tree in the sense you're thinking of, with branches and a nicely shaped crown. These non-prunable trees (there are several) look more like telephone posts with leaves than anything else - they are a series of "columnar" apple trees; they never need pruning because they have no branches. The apples grow on spurs that grow directly from the trunk.
All trees with branches will require pruning at some point - even the columnar apples may need pruning if there is physical damage to one or more spurs, of if the leader breaks. Even if someone were to develop, say, an oak that grew in such a way that its branches never crossed, were perfectly spaced for optimal light, and maintained a perfect canopy, that tree, too, would require pruning due to wind damage to branches, disease, insect infestations, and other environmental issues that affect trees.
In general, trees that grow fast (for example, Autumn Blaze Maple) require more maintenance pruning than trees that grow slow. Trees with brittle wood tend to require more pruning than trees with non-brittle wood. A "non-prunable" tree would probably have to be a very slow growing species with pliable branches.