Yeah, paradoxes are amazing, especially time paradoxes. I remember spending a night reading about all of the different paradoxes. I'll post a few time paradoxes now.
A man travels back in time to discover the cause of a famous fire. While in the building where the fire started, he accidentally knocks over a kerosene lantern and causes a fire, the same fire that would inspire him, years later, to travel back in time.
A man receives information about his own future, telling him that he will die from a heart attack. He resolves to get fit so as to avoid that fate, but in doing so overexerts himself, causing him to suffer the heart attack that kills him.
In the legend of Oedipus, it is prophesied that the baby Oedipus will one day kill his father and marry his mother. His father, Laius, attempts to circumvent the prophecy by abandoning the baby in the wilderness, where he was found by another King and Queen and raised as their son. Years later, Oedipus — unaware that he was adopted — learns of the prophecy and leaves home to avoid it. He kills a man and marries the widow, but does not learn until later that they are, in fact, his biological parents. The attempts to avoid fate result in the fulfillment of the prophecy.
A second type of time travel paradox is the closed causal loop. The classic example is the one in which you one day receive the instructions on how to build a time machine from a mysterious stranger. You follow the instructions and then use the time machine to go back in time, where, disguised as a mysterious stranger, you proceed to give your younger self instructions on how to build a time machine. But where did the knowledge of how to build such a machine come from in the first place?