Enjoyed reading about Gettier Problems in philosophy, which are instances where people hold true beliefs for wrong reasons, here are two from the link which I think are thought provoking and also hilarious in the typical analytic philosophy tediousness way:
The sheep in the field (Chisholm 1966/1977/1989). Imagine that you are standing outside a field. You see, within it, what looks exactly like a sheep. What belief instantly occurs to you? Among the many that could have done so, it happens to be the belief that there is a sheep in the field. And in fact you are right, because there is a sheep behind the hill in the middle of the field. You cannot see that sheep, though, and you have no direct evidence of its existence. Moreover, what you are seeing is a dog, disguised as a sheep. Hence, you have a well justified true belief that there is a sheep in the field. But is that belief knowledge?
The fake barns (Goldman 1976). Henry is driving in the countryside, looking at objects in fields. He sees what looks exactly like a barn. Accordingly, he thinks that he is seeing a barn. Now, that is indeed what he is doing. But what he does not realize is that the neighborhood contains many fake barns — mere barn facades that look like real barns when viewed from the road. And if he had been looking at one of them, he would have been deceived into believing that he was seeing a barn. Luckily, he was not doing this. Consequently, his belief is justified and true. But is it knowledge?
In none of those cases (or relevantly similar ones), say almost all epistemologists, is the belief in question knowledge. (Note that some epistemologists do not regard the fake barns case as being a genuine Gettier case. There is a touch of vagueness in the concept of a Gettier case.)