My favorite theorem is probably a tie between $ e^{i\pi}+1=0 $, and the Pythagorean Theorem: $ a^2+b^2=c^2 $.
The former, because it incorporates all of the major constants: $ e $, $ \pi $, $ i $, $ 1 $, and $ 0 $. The latter because, though it is first taught very early in mathematics education, and remains useful for as long as you continue to study math (at least, it has over the course of my engineering education).
