One-time pad
The only cipher proven unbreakable, and the only one almost nobody can be bothered to use.
The key is truly random, at least as long as the message, and used exactly once; encryption is XOR between plaintext and key. Gilbert Vernam patented the construction in 1917, and Claude Shannon proved in 1949 that it provides perfect secrecy — the ciphertext reveals nothing whatsoever about the plaintext beyond its length.
The price is that distributing the key is exactly as hard as distributing the message itself. And break any of the rules and everything collapses: the Soviet Union reused pad sheets during the Second World War, which let the US read the traffic for decades in the VENONA project. The method survives where the requirement is absolute and the volume small — keys on paper, cards or memory chips, destroyed after use.