This is certainly an interesting topic, so I guess I'll share my own personal philosophy on "souls."
A most basic definition of a soul is "something which can perceive, but cannot be perceived." A soul sees, hears, touches, tastes, and smells the world through the various faculties of the body, but cannot be seen, heard, and so forth. This, however, is a rather impractical definition of souls when dealing with them as a whole. Therefore, I split up a soul into three separate categories: mind, spirit and "soul" (note here that when I refer to soul, I am referring to the greater whole, and when I say "soul," I mean the specific part). All these parts interact with one another and with the body, and sometimes they overlap.
We'll start with the hardest and work our way to the easiest. The "soul" is the most enigmatic subsection of the soul. It corresponds mostly to the will of the being from which it comes. It decides what the goal in life of the being in question is. Whether simply survival or perhaps something greater, the soul is what guides us. It also holds the basic moral structure, and therefore the ideas of good and evil. However, an amoral person is not neccessarially lacking a "soul," it's just that either the "soul" is not in control, or the will part of the "soul" is completely overpowering its moralistic part. This is the highest form of the soul, and is somewhat similar to Freud's superego.
From there, we go to the spirit. The spirit consists mostly of the emotions of the person. Fears, hopes, wants, anger, happiness, contentedness, all these are aspects of the spirit. The spirit is often the driving force behind most of our primal instincts, such as the flight or fight decision. Many times, the "soul" will determine what we do, but it is the spirit which determines how we do it. For example, a soul might demand revenge, but a person with a "hot" spirit would go out on a murderous rampage, while a "cold" spirit would sit and calculate, waiting for the right moment to strike. The spirit also corresponds to Freud's id.
The mind is the easiest portion of the soul to understand. It is the part that thinks, believes, doubts, remembers, wonders, and other related functions. When I say "Cogito ergo sum" (I think, therefore I am), I have confirmed the existence of my mind. It is, in essence, Descartes' "thinking thing." The mind is also what chooses what to do, in a more local sense. The "soul" guides the person on what general action to take, the spirit tells it in what way to perform this action, but the mind is what actually goes about making the exact plan. The mind also has the power to override both the "soul" and the spirit, making it closely relate to Freud's ego.
As to how all this relates to undead and whether they have souls, I would say that it is a necessity for undead to have at least some form of a "soul" guiding and directing them. Even if it's just an insatiable appetite for brains, there's still a will guiding the body on what to do. It is possible for a necromancer to make bodies dance using only puppet strings, but it seems like it would be more efficient to make an artificial "soul" which guides the undead in the basic task which the necromancer would like to perform.
They also have to have some semblance of minds, due to the fact that they can distinguish between one thing and another, they know how to move their bodies, and they can make decisions as to which rout to take to the intended target. However, their minds appear very limited and basic, and not capable of "higher" thought.
The only thing which undead might not have would be spirits. Emotions and zombies don't seem to go well together in my opinion. Emotions and ghosts, on the other hand, do. A ghost would probably be missing more of the mind aspect, with actual enhancement of the spirit. Other undead, like vampires, have complete souls, they just are fundamentally different from ours, mainly in the "soul" area (as their will and moral code are drastically changed).
How this could be incorporated into the game....not sure.