Judai's main ability is that which stands conferred by his status as the Champion of Dark Justice. Unlike the stereotypical classification of darkness representing depravity and light as a bastion of holiness and purity, his universe completely flips the concepts around, with the Dark placed at one end of the spectrum as a benevolent force of creation, one which gave birth to all life in existence. In order to defend its fragile wards from the encroach of its opposite element - the Light of Ruin, intent upon complete elimination - the formless, shadowed energy created a living human out of its very essence, endowing him with a natural resistance towards the Light and an ability to actively control and manipulate the elemental power of darkness as an aid in his mission. This guardian proceeded to be reborn over consecutive generations, being brought into the world whenever a new confrontation between the opposing forces needed to take place, in order to keep the Universe in a state of balance. As the latest reincarnation of the Gentle Darkness' Herald, Judai possesses all of the described traits, yet was unable to actively use them for the first part of his childhood, given that he wasn't even aware of their existence -- save for some brief intuitive flashes.
As a living avatar of Creation, his abilities are loosely defined and it is presumed that they have a nearly infinite array of uses, from influencing the minds of his opponents all the way to creating life itself out of inanimate matter.
Given that he had been using them for around five years at the point where he ended up being taken from his own canon, Judai gained a good understanding of what the Gentle Darkness could do, using it in order to launch spectral attacks upon his adversaries in the forms of bolts, tendrils and waves of black power. Another application which presented itself to him was the ability to forcibly gain entry into an individual's mind and tamper with what could be found there - yet such was a course of action that he refused to take and still does so at the present moment, considering an individual's mind to be hallowed ground, no matter how vile the person in question might happen to be.
Along with his power of darkness, Judai has an innate ability to see and hear Duel Spirits, the ethereal creatures which exist within cards - yet whether this gift of his is linked to his status as a child of the Gentle Darkness or merely an affinity towards the more esoteric planes of existence remains entirely debatable. Linked to his communication with Spirits is Judai's unusual prowess in the game Duel Monsters -- an instinctive inclination towards the strategic aspect and a knack for easily picking up new combinations or guessing an opponent's own moves, if he happens to be familiar with the overall goal behind them. However, what gives Judai a definite edge over his opponents is the power of the 'God-Draw' - a Duelist favored by Lady Luck can draw his saving card in almost impossible situations. Such was an ability that Mutou Yuugi displayed as well - and whether it is merely luck or a result of a deep spiritual bond with one's Deck has yet to be determined.