The first character I played, at first I seem to recall the npcs had audible voices, not just text. But now, none of them have any audible voice. Was I imagining things? It would be nice if my bridge officers could speak to me when they provide mission updates.
The Khitomer EMH had a voice over, and Admiral T'nae had a voice over. The Cloaked Intentions story arc also has voice overs. There is talk that they will go back over some of the PvE missions to add voices and cutscenes that were pioneered in the Cloaked Intentions missions.
during beta they had VOs for all the BOFFs and some of the other NPCs, but there was a compatibility issue, so they were removed before the game officially launched. They had planned to fix them, but the devs had to back burner the VOs in favor of more critical bug fixes. I think they gave up on trying to fix them though, because IIRC the BOFF VOs aren't being listed on the engineering reports anymore.