No. 2 Half-Life 2 Episodes 1 & 2 (PC, also on X-box (HL2) and 360 & PS3 in The Orange Box)
Sequel to what is probably the most innovative FPS to ever grace the market, Half-Life 2 had a lot to live up to, but boy did it deliver. When released, the animations were some of the best ever seen, the graphics were superb even on a low spec PC, the physics implementation was revolutionary, the characters felt real, the battles were suitably epic in scale and it introduced the superb concept of the gravity based weapon.
Much like the original, HL2 retained the immersion by sticking to the first-person perspective. As the silent protagonist Gordon Freeman, you had the chance to let your imagination place your own persona into the image of Gordon Freeman. However, Valve took this concept and blew it out of the water with its dystopian setting and storytelling. Hidden extras in the world reveal tit-bits of info on the story and events leading up to HL2 and potential events in future games. You are always Gordon Freeman, so when if you miss them, Gordon misses them. Control of Gordon's movements is always with the player, so when Gordon's physical abilities are impaired the feeling of being powerless is amplified. This is done well near the end of HL2 but utilised expertly throughout Episode 2.
Another factor that I think is often overlooked is the acting and animations of the characters. In most games, the acting is terrible and the characters feel like they're just generic plot devices. In HL2, the characters actually engage in real life actions. The actions of Alyx are where this is most apparent. Yes she's with you (or Gordon) and talking to you through large segments with good animation, but also little details like when she's teleported to her fathers lab and she smiles and gives him a kiss on the cheek. Easily missed, but little details like this help to breathe life into the characters.
I haven't even mentioned the superb game design Valve implement where early on they allow you to explore an area to get the lay of the land before entering a gun fight. Or the immense battles vs soldiers and gunships on dystopian rooftops closely followed by mass battles with striders. Or the well paced vehicle sections where just as they start to get boring, you move onto something else. Or the little puzzle sections that give you breathing room. The sheer variety and depth in the game is epic in every sense of the word. No other pure FPS does what Half-Life 2 manages in a single package.
Add to all this the fact that Valve are continually updating the Source engine and many little improvements are seemingly retrofitted into Half-Life 2 and Eps 1 & 2 (via Steam), and you get the greatest FPS package on the planet.
