"I know one thing," Socrates famously said, "that I know nothing."
This statement is a paradox in itself, demonstrating complexities of self-referential statements; but it also suggests an insight from one of the founders of Western philosophy, that you should question everything that you think you know. Indeed, the closer you look, the more you'll start to recognize paradoxes all around you.
We've picked our favorites from Wikipedia's epic list of more than 200 types of paradoxes.