1. Common Sense Skepticism: Simply the realization that none of us can know everything, and because of this we are well advised to be doubtful about some things.
2. Philosophical Skepticism: The tendency to doubt or deny some particular philosophical claim.
3. Religious Skepticism: Historically, the word has often been used of those that deny or question religious truths. Synonyms: Freethinker (one who will not accept a doctrine on authority, but demands empirical proof), atheist (one who positively denies that God exists), agnostic (one who claims that we cannot know, or we happen to not know, or he happens to not know, whether God exists), unbeliever (someone who has no opinion about the existence of God).
4. Direct Skepticism: The conviction that there is some necessary condition of knowledge that cannot be fulfilled.
a. "X is true" -- perhaps it is impossible to know anything about truth.
b. "Y believes that X is true" -- maybe belief is impossible. Or, maybe the only belief that counts is certainty, and that is impossible. Operating on the basis of probability could count as skepticism -- it is part of what makes Hume a skeptic.
c. "Y is justified in believing that X is true" -- maybe there is no justification procedure that will suffice.
And there are several forms of direct skepticism:
a. Knowledge is beyond reasonable proof. This is the weakest form. It says simply that knowledge cannot be demonstrated. It says nothing about whether there is something that can be known.
b. Knowledge is highly uncertain. This says not that there is no proof, but that the proofs contradict each other.
c. Knowledge is totally impossible. Perhaps the knower cannot access reality at all.
5. Iterative Skepticism: A person could know something, but that person may not know that he or she knows it.
6. Pyrrhonian Direct Skepticism: This is the view which refuses to commit itself with regard to the epistemic status of any proposition, including the position that Y cannot know that X is true. This position asserts that there is no better reason for believing that Y can know X, than that it is not the case that Y knows X. Therefore, we should just suspend judgment.
7. Perhaps one can be skeptical toward knowledge, but not towards justified belief. In other words, maybe we cannot know something, but we can be justified in believing it because of past experience, corroboration, or whatever. This would mean that we could operate in the world (justification gives us reason to continue), but we could not claim knowledge.
8. Following on the idea that knowledge is true justified belief, one particular form of justification could be at issue. For instance, a skeptic could simply claim that knowledge cannot be grounded on authority, or on empirical evidence, or on a priori knowledge. In this sense, virtually everyone is a skeptic, because everyone will prioritize one form of justification over another.
9. It is possible to have skepticism based on the denial of the traditional nature of the object of knowledge. We could call this "sociology of knowledge". For instance, one could say that we cannot know anything because knowledge itself is conditioned by power (Nietzsche, Foucault), desire (Freud), economic conditions (Marx), or whatever else. This undermines both the object of knowledge, as well as the human capacity of reason.
10. There is also what we could call methodological skepticism. A person could be a skeptic because this person could claim there is no reliable method for attaining knowledge. Either a method would have to lead to certainty (and none does), or it would have to lead to a significant probability (and none does).