This is a marvelous story about Einstein's first proof of the theorem. It relies on symmetry and the similarity of right triangles. This proof is easy to follow and quite elegant, and the article suggests that reasoning from symmetry foreshadowed Einstein's later work in the geometry of spacetime.

newyorker.com

This is the first proof that I learned. It is completely straightforward, and can be cut out and worked with actual paper. It also shows the "c" square so it makes a lot of intuitive sense.

mathsisfun.com

This one is perhaps my favorite. First, it is unexpected because it uses an unusual configuration of shapes. Second, it is simple because it is based entirely on the area of triangles. The only drawback is that it makes it a little hard to see the squares that arise from the actual Pythagorean Theorem.

io9.gizmodo.com

OK, not really a proof at all, but I like this because it gives some insights into Euclid's proof. The proof is ungodly complex as it involves slicing the triangles and associated squares into other triangles and rectangles, and it relies on previous results from Euclid's work. However, it is kind of the gold standard, and this painting shows both the complexity and the ingenuity.

americanhistory.si.edu