If you like your first person shooters hardcore then get STALKER: Shadow of Chernobyl and the Clear Sky expansion.  Play the singleplayer for an hour or two to get the feel for the controls, then download the Oblivion Lost mod which makes the game a bajillion times better by allowing you to do things like repair equipment, drive vehicles, introduce unkillable NPCs (STALKER is one of the few games with truly unlimited AI so monsters and enemies roam and important NPCs could be killed before you ever reached them), and random blowouts. 

STALKER also wins my own personal award of "Creepiest and Most Atmospheric Game Ever" and it can't be experienced in its full glory without running the game on max.  For example, there's an enemy in the game that only hunts at night or in dark areas like sewers and it's completely invisible when it's not attacking.  Unlike most games which would have the creature attack you on sight, it actually stalks you through the level and waits until your back is turned or you got injured from a fight with another monster before fucking assaulting you and it only turns visible when it attacks.  You can see the outline if you're about 2 feet away but by then it will start to attack and the only other cue you get are these squishy footsteps and a low groan.  I nearly shat my pants when I first saw it. 

It's not for everyone, especially people used to Run N Gun BLOW SHIT UP games, because STALKER actually uses physics and trajectory angles for the bullets meaning if you're moving at all while shooting you're probably going to miss even at close range.  The AI is also some of the most advanced in gaming and to someone who isn't used to enemies using the surroundings and constantly flanking it will be hard as hell.  Think of the game like Oblivion meets Half-Life and play it very slowly because if you charge through with guns blazing you'll get your ass handed to you on any but the easiest difficulty setting.

In the same vein as realistic shooters, I always recommend Armed Assault (also called ArmA) which is the spiritual successor to Operation Flashpoint.  It's a military shooter, meaning 1-2 shots and you're fucking dead, but it's a game on a epic scale and you can switch between soldiers.  Battles are HUGE as they take place in this 30 square mile map so you can begin a mission by scouting through a forest, doing light skirmishes with the enemy, call in tank reinforcements from a base several miles away, blitz through a large city, then call in an air evac at the beach.  It also comes with an editor and while the game isn't super popular like Left 4 Dead it has a pretty sizable cult following of super dedicated hardcore gamers and online matches are a blast.

As far as underrated games go, King's Quest came out last month and I love that game.  It's turn based strategy/RPG, so it might not be your cup of tea, but there's no building (you buy/find units and explore/kill monsters) and there's plenty of units to experiment with so it doesn't get boring too quick but you probably won't want to replay it any time soon.

Finally, if you're an FPS fan then you'd be pretty dumb to miss out on Crysis.  It thought it was alright.  Nothing spectacular or mind blowing but above average in that it was a shooter and it did what it set out to do well (provide pretty graphics while you shoot shit).

There aren't many PC exclusives anymore because faggy developers think that the market is dead thanks to piracy although they fail to realize that their anti-piracy measures piss off the honest people who actually buy the game since pirates just download a crack and never have to deal with it.  I would normally recommend Sins of a Solar Empire but since you don't like RTS games that's probably waaay out of your league.  I can't really offer anymore games that don't also exist on the 360.

EDIT: Oh yeah, I forgot about The Witcher which is also PC exclusive and pretty fun.  The recent patch fixed all the dumbshit from the original release (load times are no longer a kick in the balls) and while it's a "different" RPG experience, I definitely enjoyed it.  Drakensang, the latest Dark Eye (Realms of Arkania in America) is being released in the US in February which has me kind of excited because I rather enjoyed Neverwinter Nights 2 and it plays out similar to that except with better graphics and a more interesting world to explore.  Speaking of Neverwinter Nights, another expansion pack came out recently but I haven't had a chance to play it.

ArmA has a pretty long singleplayer campaign so the answer to your question is yes; it's not all multiplayer.  The game has a gradual ascension from lowly grunt to team leader (where you bark the orders) to tank commander to pilot and it's just a really big and epic game.

Don't be fooled by Valve's 'You Save' calculations. It's GENERALLY cheaper to buy L4D + Orange Box + CS:S + HL1 (buying this retail and adding CD key to steam adds ALL expansions for free) seperately from online retailers than from steam. It MIGHT be about the same price in America (haven't worked this out yet) but pretty much everywhere else in the world it's like $50 more for the complete pack.

You can easily buy those games on the secondhand market cheaper than what Valve is selling online but then you'll be supporting the 3rd party distributors and as a close friend of Mike Capps I cannot take the stealing of money from hard working developer's hands lightly.

Buying used games is the same as piracy, people.

lol

I liked "Call of Juarez", and "Gun" though it is mostly third person. However, it plays like an FPS, and does bullet time in first person. Two of the best western games on any platform, ever.

I'm not usually an FPS fan, but I picked up the Painkiller series for $20.00 (Canadian) and it has been, by far, one of the best video game investments I've made in a long time. Granted, I couldn't care less about the story but I am thoroughly enjoying the gameplay. I haven't gotten to the second game yet but I'm looking forward to it.

Painkiller is what Doom 3 and Serious Sam 2 should have been.