Typically, when people say they are sceptical about something, usually what they mean is that they feel they have been given insufficient reason or evidence to believe in the truth of some particular claim. For example, if someone were to say to me that they are an astronaut, I would be inclined to be sceptical since being an astronaut is very unusual. If, however, the person were able to provide me with further evidence, for example showing me some appropriate NASA insignia or other documentation, then my scepticism would be mollified, and I would be much more inclined to believe their claim. This is the key defining feature of ordinary scepticism, namely that it can be reduced or eliminated by providing more compelling reasons or evidence. This is different to most forms of philosophical scepticism, which, as explained below, typically claim that there cannot in principle be any possible forms of evidence which could justify certain types of beliefs.
A local skeptic rejects knowledge claims within a certain subject matter or domain. For example, a moral skeptic beliefs that no one is justified in believing any claims about moral matters, perhaps because they believe that human beings cannot have any access to truths in the moral domain. A theological skeptic may believe that no beliefs about god can be justified, perhaps on the basis that human cognition is far too limited to be able to access any divine truths one way or the other (this is typically the position of the agnostic, one who claims it cannot be known whether or not god exists). In theory one can be a local skeptic about any particular type of knowledge, whilst retaining beliefs about other forms of knowledge.
Global scepticism, sometimes also called academic skeptism, is the most extreme form of scepticism, as it applies local scepticism to all forms of knowledge. In its strongest form, the global skeptic believes that only one belief can be justified, namely the belief “no beliefs can be justified (except this one)”. This is the idea behind Socrates’ famous assertion “I only know that I know nothing”. The global skeptic is maximally pessimistic about knowledge claims, believing that all knowledge claims fall short of what would be required for them to be truly justified, and hence must be discarded as not really knowledge. It may still be that case that the global skeptic retains beliefs about a great many things, but they will argue that such beliefs strictly speaking cannot be rigorously justified, and so do not count as knowledge. While this may sound like an absurd position, and indeed very few philosophers have ever endorsed it, much work in epistemology has been devoted to devising responses to global scepticism.
Pyrrhonian Skepticism is a particular variation of global scepticism, which its proponents argue is less dogmatic. The key distinction between Pyrrhonian and global skepticism is that, while global skeptics claim that they can give justifiable reasons for why no beliefs can be justified, the Pyrrhonian skeptic does not. That is, where the global skeptic says that no one can have justified beliefs, the Pyrrhonian only says that they themselves do not have any such beliefs, without making any claims about what other people might know now, or what they or others might come to know in the future. In short, where the global skeptic claims “no one can know anything, except this”, the Pyrrhonian merely claims “I do not know anything”.
Scientific Skepticism is an approach to reasoning whereby claims are regarded as unproven unless and until a sufficient degree of evidence can be provided for them. This type of scepticism, as the name implies, underpins the scientific method, and the absence of this type of scepticism typically defines pseudoscientific endeavours, where claims or phenomena are accepted as true or real without requiring sufficient rigorous evidence. Scientific scepticism is not as extreme even as pyrrhonian scepticism, as it makes no claims about our inability to know. Rather, it simply is an epistemologically conservative position, abstaining from belief until sufficient evidence (especially, not not necessarily limited to, scientific evidence) is available to demonstrate the likely truth of a claim.
Scientific skepticism, CSICOP, and the local groups: accessible overview of the approach of applied scientific skepticism in assessing paranormal claims
Skepticism: useful article detailing the key ideas, historical development, and different forms of skepticism
The brain in a vat argument: Internet Encyclopedia of Philosophy article discussing this famous argument for global skepticism
How far can skepticism go?: a brief discussion of the extent and limits of skepticism from PhilosophyOnline.co.uk
Ancient skepticism: Standard Encyclopedia of Philosophy article covering Pyrrhonian skepticism and other ancient approaches to doubt
What skepticism reveals about science: Michael Shermer discusses his views on scientific skepticism in this article from Scientific American