Let's start with which abilities we've seen and assume to be human. Generally speaking we know that reinforcement is a power. Reinforcement is defined as the amplification of an existing trait. So Trinity can be faster, stronger, etc. than cops. The other major category of human abilities fall under telekinesis (the manipulation of physical objects with the mind) such as floating blocks and bending spoons. A possible additional category is Extrasensory Perception. Examples of ESP could include the blind man (if he's human), Neo responding to "Wake up, Neo", the Splinter in the mind, and finally The One's speech at the end where he says "I can feel you now." There are basically two approaches we can take to these powers:

Unified Power Theory

We say that there is one and only one human ability. Amplification. This encompasses reinforcement, TK, and ESP. The fundamental precepts of this view is that humans actually have TK and ESP outside the Matrix, but a side effect of the Matrix being a perfect simulation is that the latter two abilities can be exhibited inside under the same principles. Alternatively the deterministic nature of the Matrix enables such abilities.

Two Fundamental Powers Theory

Analogous to the four fundamental forces, we don't endeavor to understand completely at this point because it is untestable beyond a certain limit. The two Power categories would be Reinforcement (amplification of known abilities) and Psychic (TK and ESP).