Encrypting twice with same key gives back plain text
These block ciphers are called involutional ciphers, after the (mathematical) involution property of a function. This article shows a cryptographic analysis of two of them: Khazad and Anubis.

Neither Khazad nor Anubis  seem to be broken at the time of writing, basically they use the same internal structure for normal block ciphers, replacing the inner components with involutional ones.