Atbash
Mirror the alphabet. A becomes Z, B becomes Y.
What it does
Atbash reverses the alphabet. The first letter maps to the last, the second to the second-last, and so on. Because the mapping is a mirror, applying it twice returns the original text, so there is no separate decode step.
Where it came from
It is one of the oldest ciphers on record, originally applied to the Hebrew alphabet, and the name comes from its first two substitutions: aleph to tav, beth to shin. It appears in the Book of Jeremiah, where Sheshach stands for Babel.
What it is good for
Puzzles, and demonstrating that a cipher with no key at all is not a cipher in any useful sense. Atbash has exactly one possible transformation. Anyone who recognizes it has already broken it, and any tool will try it automatically.
Like every simple substitution, it also preserves letter frequencies and word shapes, so even someone who does not recognize it will get the plaintext out of a frequency count quickly.
Related
ROT13 shares the self-inverse property but rotates rather than mirrors. Caesar adds a key, though not enough of one to matter.