half life 2 firstly, one of the only games i've ever played and actually liked the characters. It has to be mentioned, though, that after listening to commentary, the HL2 guys spend ALOT of time figuring out how the characters should act for audience benefit, also the soundtrack gets you into it and the little tidbits like an area with a chair, a bear and a grenade crate over a pit of zombies, creating a back story for an unknown character that only perceptive players will notice? thats just epic.
Amnesia, of course, because it is designed to be immersed in like someone before me has mentioned. Also the controls help you to get immersed because to hold objects you actually have to hold the mouse button, unlike some games where u just toggle picking an object up and dropping it with 1 key.
Screaming "Why won't you fucking die!" at a game reminds me of how i react to alot of PvP games, especially WoW with its balance issues. Doesn't give me any sense of being immersed, just wanting to win.
Portal needs a mention, Glados and all her commentary just kept me enthralled. As well as the same effort that was being put into it as was put into HL2. again i realised this from listening to commentary.