The first two games in Thief-series. Great audio, game world, and minimal HUD. Perhaps the odd devices in the second game, and hearing your own character talking, lower the immersion a bit, but that's nothing major.

Put high quality headphones on, and turn out the lights... so far, nothing beats Thief.

I was really flashed into Star Wars: Knights of the Old Republic, Baldur's Gate II - Shadows of Amn and The Elder Scrolls: Morrowind, and Oblivion. KotOR has great storytelling and outstanding characters/personalities. I could have imagined more freedom and non-linearity but it works as it is. BGII was very atmospheric, the painted 2D graphics was way better for immersion than the 3D of rpgs of its time. For me, the TES games are exceptional in the free-roaming scenario. I prefer larger open areas and less closed up dungeons/caves and the always present sewers( - who came up with that place by the way -).