What are the different types of Junglers?

Patches as of late have drastically changed the environment of the beloved jungle. One patch, an tank-intended item promotes a tank meta. A few patches later, assassins resurface with a vengeance thanks to a major item change. These items have had unintended consequences. While an elite few dominate with said items, unpopular picks who were meant to benefit still struggle to compete.

So what if jungle items were further diversified to fit the different kinds of junglers? A nerf aimed at a particular fighter-mage wouldn't invalidate all other mage junglers; a buff meant to bring up an fighter-tank wouldn't be abused as readily by marksman, let's say. If the items are more localized, it'd be easier to resolve problem champs. Imagine if assassins were offered the choice of two items, best fitting either an autoattack-reliant champ (Master Yi) or an ability/burst champ (Rengar); a nerf or buff wouldn't push out the other.

This is a theorycrafting thread. What are the different kinds of junglers, and what'd appeal to them and benefit mostly them?