S.T.A.L.K.E.R. was quite immersive, and very well made. Starcon 2: The Ur-Quan Masters had an excellent plot, and real emotion, it's hard to tell. I'm not really affected by games all that much in those regards. I mean, S.T.A.L.K.E.R. had it's atmosphere, but I am generally a hunter and a looting type (so I'm not creeped out that easily, especially if loot is involved), and I also tend to give myself little challenges here and there (like goomba-stomping a bloodsucker, or wearing light armor most the time) or doing silly things like luring boars and other NPCs into anomalies.
Another candidate for immersion and plot has to be the X-Wing series (especially with the plot included) as well as the Mechwarrior (not Mech-Assault) series. Lots of buttons, lots of involvement, lots of piloting skill necessary to go through, and a good handling of a joystick is necessary. When big battles come along, you're really feeling desperate to survive, or spare as much of your crap as possible (especially if you're playing as a leader in the Mechwarrior games, where you have to manage what you have, pay for repairs, and etc.), but the salvages by bonus missions and etc. were damn worth the trouble in the long run (Salvaging an Atlas or Thor mech anyone?). With X-wing (Alliance, or Tie Fighter), the giant battle scenes (Death Star missions, for example) are truly immersive, and you're just hoping you don't run into a starship accidentally while taking on a squad of TIEs while another squad is chasing you; all while a Star Destroyer is shooting at you and a Calamari Cruiser at the same time.
EDIT:
Great, now I want to continue my game of Tie Fighter or try to get MW2:M running again. I miss my Warhawk; and in Tie Fighter, in no more than 2-3 missions, I'm a freaking lieutenant already, and in a good seat in the Emperor's secret service.