I do also in private, but I whisper it (mostly because I'm scared people will hear me!).
I conciously do it to 'vent' the things I wished I'd been able to say (or to try to resolve something that's worrying me), throughout my day; I mostly say very little, so being able to do this is quite cathartic.
I'm not really aware if I do it in public, but I have found myself stopping what I'm doing and having a 'sense' (and a feeling that my mouth has been moving in speech, if that makes sense!), that I have been speaking my thoughts out loud.
I really hope I don't do that, but my mind is constantly racing with words and thoughts that some of them must, surely slip out sometimes!