Underwater ambient sounds play just fine but cave ambient sounds don't seem to play properly. They can be played with the /playsound command but they don't play naturally.
I had been trying to get them to play naturally for about an hour by going in and around dark caves and in the nether but they didn't play naturally. I also had the subtitles on but nothing showed up there. The slider for the Ambient sounds was at 100%.
I saw some previous bug reports on this issue and it says 'RESOLVED' but the sounds still don't play naturally in the most recent snapshot.