Cantonese

Cantonese was a dialect of Chinese that was spoken by Captain Chin Lee. The Third Doctor once had a brief conversation with her in the dialect. (TV: The Mind of Evil)

The Fourth Doctor stated that he could speak Cantonese, among other Chinese languages. (TV: The Talons of Weng-Chiang) A version of the Doctor from a parallel universe could also speak Cantonese. (AUDIO: Sympathy for the Devil)

Behind the scenes
Chin Lee actor Pik-Sen Lim actually spoke Hokkien natively, not Cantonese. Meanwhile Fu Peng actor Kristopher Kum spoke Cantonese natively, not Hokkien. The actors therefore were speaking each other's native dialect. This odd role-reversal occurred because the original Fu Peng actor was fired after location filming but before studio recording. The other Mind of Evil actors — and especially Jon Pertwee — had already learned some bits in Hokkien and some in Cantonese. Since switching them at a late stage would have been difficult, the two ethnically Chinese actors used each other's linguistic expertise to perform a seamless swap. (DOC: The Military Mind, DCOM: The Mind of Evil)

Cantonese is one of the few real world languages to be subtitled in televised Doctor Who, since it is generally assumed that the TARDIS translation circuits are naturally giving everyone in any given scene mutual intelligibility.