Answer:
There are many kinds and definitions of paradoxes, and many are variations of others. The most famous is Russel's Paradox, which revolutionised logic and set theory.

Russel's: Does the set of sets that don't contain themselves contain itself?
Barber: The barber shaves men who do not shave themselves. Who shaves him?
Liar's: "My fellow citizens, I am now lying to you"
Coastline: The smaller the ruler, the longer an island's coast is.
Arrow information: You need to understand the info you're buying before you buy it.

...and many more. There are economic, political, topological, and even astronomical paradoxes that are actually quite entertaining.
First answer by Sherlock310. Last edit by Sherlock310. Contributor trust: 5 [recommend contributor recommended]. Question popularity: 2 [recommend question].