This would be great if you wanted to talk to yourself without anyone understanding what you’re saying, for example, or if you didn’t want anybody to know what you were writing down. It might also be useful if you enjoy lots of foreign language media (see music, tv shows, movies) and want to experience the “original” rather than through dubs and subs.
Personally, I would go for either Russian or Estonian, both of which are because I frequently listen to lots of music that are in those languages, and they aren’t spoken by any of my friends.
Hungarian, so I could have a good conversation with my lovely stepfather, whose English isn’t great.
Cantonese and/or Mandarin for chat with Chinese friends and relatives.
What I really want though is a babel fish - you put it in your ear and it acts as a universal translator. Any language, Earth or alien.