Here is a list of games that you are likely to receive on this
For my money, the most immersive game around at the moment is Risen. The story is simplistic, the answer to most problems in the game is 'yet even more violence', but the main story is beautfully woven into one of the most stunningingly artistic fantasy worlds you will ever see and combining this with the brilliant arcade combat action, you have an absolutely wonderful immersive game. I am currently totally lost in it spending far too many hours per day running around the volcanic island of Faranga. However, I would recommend only the PC version (console is shockingly low quality in comparison) and I would also advise that I wouldn't expect that you would get particularly fantastic performance on your rig (so if you are a 60FPS only guy like I am, I would avoid this one for now).
I'll support Mat here about Risen. It(for the most part, or at least near enough) looks like you're running around a middle ages/Spanish inquisition version of Crysis(you'll notice a lot of familiar art/texture use!).
You just have to give it a few days of playing and get to moving about the island to understand what you're doing and etc. While the game play is a bit arcadish, that also works in your favor. The combat is simplistically repetitive, which is good, considering you can melee combat or use magic.
The story is also pretty neat and twisting. For a while you think and act in a very short-sighted manner, worrying about things that seem important, but as the story unfolds and you realize the true nature of things, those once imperative issues become petty.
Mount and Blade was also great. It's proper medieval combat but with the feeling of an MMO. Of course being offline, it's your world all to yourself. The key to this one was the combat. Now if only they could make an actual MMO like Mount and Blade. I believe the closest we had was Darkfall or Mortal, but they fell victim to MMO woes.
My last recommendation would be
Fallen Earth. The main story is actually quite deep and stays with you forever based on your nature. While the game is still a modern MMO at heart, with similar redundant pitfalls and foundations as it's competitors, for most people it's still different enough that it's worth the hours you put into it. And by that I don't mean lots of hours. Rather I'm speaking quality vs. quantity. You can achieve so much in the game compared to other MMOs in such a short time - because of the different things you would do or want to do. That doesn't mean things are easy or fast or 'extreme,' rather that there's lots you can focus on (or NOT focus on).
The 'world' is very expansive and large, almost desolate and infinite feeling. Combine that with the fact that you can make yourself completely self sufficient and independent from things like auction houses, merchants or other players, and it's almost like an offline game, with the benefits of patching, maintenance and content additions. To me that's pretty awesome. After years of group and clan dependent games, doing things by yourself is great. Thus the time you spend is all about you, hence quality vs. quantity.
Ones i won't recommend are :
Aliens versus Predator: If you love the series and or the old games, you'll enjoy it but also be very disappointed. It doesn't have the same suspense or feeling 1 and 2 did. It's kinda like this: In the first two games, as a Marine, your pulse meter was your lifeline, literally. You would hunker down in dark corners of the colony base tunnels and just sit for minutes on end watching, praying there were no blips on your pulse display. In this version, you run around in rather bland areas, and you see/hear a blip. Instead of freaking out, you sorta just shrug your shoulders and take the aliens head-on. Something about punching an alien in the face that actually hurts it, doesn't seem plausible. -Rent or borrow from someone
Bioshock 2: Story wasn't eventful nor twisting. Plus the action didn't make sense given that you play as a Big Daddy, and furthermore, you knew what to expect from the world of Rapture. In Bioshock 1 you didn't and thus you were surprised. -Rent or borrow from someone
Mass Effect 2: Fun, but not as involving as the first one. Again, probably like Bioshock, it's because you knew what to expect. I will say however though that "involving" isn't necessarily the same thing as "immersive" in this case. You don't really get INTO it, but the story has some epic moments for sure. Buy it if you like the series, if anything so you can beat the game and prepare for Mass Effect 3.
STALKER: COP : Like always, it's a niche game. I didn't find it overall better than Clear Sky, but it has some advantages/benefits. Unfortunately you're reduced to having to use third party mods in order to make it play like it should, and that's just not right - not after they've had three tries to get it right. -Buy it if you like the series, otherwise just use Clear Sky with mods.
Metro 2033 : Obviously a contender for most graphically challenging game title at the moment, however has some serious base flaws. It's extremely linear - which would be ok if the action and story supported it, but it doesn't. The action is cool at the start, especially when you encounter bandits or militant groups, having to bob and weave through the dark, and listen for footsteps and watch for crossfire and etc. In amongst the environment(s) the action gets intense. However as the game goes on and the story unfolds, you run into hordes of mutant creatures that more or less swarm in silly numbers and run around jump-slapping you in the back of the head as if they're just toying with you. You spend most of the time spraying all over the dark trying to stop the onslaught. If they'd strayed from the book/story and excluded the mutants, and kept it about civil/militant post apocalyptic strife between humans, then it would have been really great.
Additionally the story, much like book makes no sense. And when it's over, you're kinda sitting there thinking 'what the hell?' -Rent or borrow from someone
Borderlands : Very cartoonish game play, and supported by cartoonish art. The original visuals were far superior. It's got some neat weaponry and gun play, but they hyped it up a bit too much with the discussions about 'free roam' and etc. -Rent or borrow from someone
Battlefield 2 : Don't get this game with only single player in mind. While it's got some moments of decent action and there are some environments(like the daytime field run back in the 1940s sequences)which are nice looking, it's almost like a poor man's Call of Duty. A few visual features are better than CoD series, but it doesn't pan out like a lot of the screenshots would suggest. This is for online play really, much like the CoD series, but at least with the latter day CoD games, while their action is horrendously face paced and awfully unrealistic, it at least at times can be dramatic(whether single or multi). Bad Company 2 has a few moments there, but mostly falls on it's face.