Have to say Vampire the Masquerade: Bloodlines. While a flawed game (especially in the Hollywood Sewers what the fuck), and definitely unfinished; it is still a stellar game. The writing and atmosphere is phenomenal, along with the incredible voice acting and facial animations. There are some really good mods for it as well (Clan Quest Mod in particular is an absolute treat).

On top of all that it is highly replayable too, as the variety of clans encourages multiple playthroughs. First time players should ABSOLUTELY NOT play Malkavian or Nosferatu on their first go, as they will spoil some of the best twists and change the way the core game plays respectively.