There have been a number of other interpretations here in the response to this question on Quora, many of which are layered in the long history of these multiply retranslated passages.
To my way of thinking, the original sin of Adam was not in knowledge nor in the act of eating the fruit of the tree (The tree is literally called "tree of understanding of good and evil"- טוֹב וָרָע "tov v'ra", good and evil) and Adam is prohibited from eating of it under pain of death "within that day" (2:17) before Eve is created (2:22), so Eve did not hear the command first-hand. We know that Eve has received this knowledge second hand from Adam because she does not refer to the tree by the name God has called it, "thou shalt not eat of the tree of knowledge of good and evil" she says (3:3) "the tree in the center of the garden" בְּתוֹךְ-הַגָּן implying that Adam has relayed the information incompletely or has pointed out a different detail than God has mentioned. She adds an additional proscription- "do not touch", which was not one of God's original commands.
Furthermore, we know that they are "naked", but they don't know that yet. But are they truly "naked", or simply capable of being "crafty", "cunning" like the serpent, and don't know it yet?
So let's put all those pieces together. Eve has received second hand knowledge from Adam saying "don't eat or you will die" but it is not explicitly said that he shares that it conveys knowledge of good and evil. The serpent says "that's not the whole story, it conveys knowledge of good and evil", and she eats. (In fact, the serpent is telling the truth, but it is possible to tell the truth in a way that induces someone to make the wrong choice, an interesting side discussion but I will leave that alone.)
Now, the next thing they both do is hide themselves from God. When confronted, Adam says "i'm naked!" (which, to my way of reading, is him yelling "I'm wily!", not an unusual experience I have heard from parents of young children) and when God asks the direct, yes-no question "have you eaten from the tree I commanded you not to eat" Adam answers "You gave me this woman, and she told me to." This is a behavior pattern you see in children who are first learning about how to handle things they find out for themselves but were prohibited from exploring. First, you hide from authority, and then blame it on someone else and/or the authority figure. It's about accountability- when first created, they are accountable, "are naked", but don't know it. They then get knowledge, and begin to realize their own accountability and role in what they do, and their first reaction is to deny and defer.
Many people interpret "naked" to be "you should be ashamed of your nakedness" but in reality it's something a lot more like "you should be ashamed of your guile, your aversion to responsibility, your dodging and blaming others". The original sin is not eating of the tree, but in denying responsibility for it. Both Adam (who in theory knows better) and Eve (who was told not to without knowing why) are suffering from Adam's sin, (...Eve quickly follows Adam into sin because she then passes the buck to the serpent, and because she is drawn to Adam and doesn't think for herself) as well as the deceiver, who knew better and understood the consequences.
Anyone who watches the behavior of children realizes that we are not born into sin, but learn it from others- the child does not hide after having broken something until after the first time we punish them for it. It is our innate ability to create our own downfall that is the original sin. It's our capacity to do the wrong thing, to lie, to defer blame to others, that is our greatest problem.
So, to answer your question, what is the forbidden knowledge? In this story, it is the guile, the ability to lie, that is inherent. In fact, in this story, God has spoken a exaggeration/mistruth too, because he said "if you eat, you will die in that day" and this does not happen until much later, many years later (5:3). If I wanted to take a Manichean bent (I do not), I would say that God created sin with His first inequality, having given special knowledge to Adam but not to Eve. (In some circles, this would lead to a fascinating feminist critique.)
It is unstated, only presumed that the knowledge itself causes you to die: I don't agree with this point of view. The punishment is that of suffering with the knowledge that life in the Garden was easy and only had one rule, and instead you have to work for a living, "toil" and "travail", and suffer to find out the rules through experimentation. All men die (and I argue that Adam would have died anyway in the Garden, but never got the opportunity, because as humans we do mature into knowledge as we grow up), but not all men have to suffer or cause suffering, only the cunning who do the wrong thing despite knowing how to be better, and being complicitous in acts they know to be wrong. Being crafty may be doing wrong when you know what is right, but suffering is also caused when you don't communicate the whole story, accurately, on what is wrong to innocents.
To my thinking, the knowledge is of sin- and in this context, sin is having the choice to do the right (good) thing and do the wrong (evil) thing deliberately. Doing so gains you knowledge (once you break a plate, like that child, you know you shouldn't fling them carelessly), and shame- because once you realize you're erred, you feel bad about it. This is consistent with Eccl 1:18- "he that increaseth knowledge increaseth sorrow." http://www.mechon-mamre.org/p/pt/pt3101.htm But knowledge itself is not sin- having the ability to be cunning does not mean that you have to exercise it. Adam had the choice to own up to what he learned- eating does not cause you to die- and come clean immediately with God. But he chose not to- and the fact that all of us fall into this mistake, of being deceptive, is the reason we suffer/toil. Truth outs a harm immediately and in most cases, that original harm, once outed, is easily correctible and doesn't degrade into something more sinister. But knowledge and sin are very closely entwined, and the story is attempting to convey the many levels of nuance involved in cunning.
We are all "naked" before God in our behaviors and actions, and I say, we are born innocent. But eventually we learn sin, just as Adam and Eve did, because we are social animals. What is good and/or evil, is not that we sin, but that we don't take accountability for our ability to sin, and choose to do so no more.
from my post on Quora: http://www.quora.com/The-Bible/What-precisely-was-the-knowledge-that-God-didnt-want-Adam-Eve-to-have/answer/Matt-Harbowy?srid=hoC6