Well, as most people here have already pointed out it's sort of all about genre really. FPS in itself is more a concept than a class of games.
I mean, hell, Spyro: Year of the Dragon has FPS elements in it.
Some of my absolute favorites that I'd recommend to anyone at any times are:
Battlefield: Bad Company 2
Crysis / Crysis 2.
Half-Life, if you like classics, or Half-Life 2, which in my opinion is the best video game to date.
And if you'll allow me to get a little abstract: The Elder Scrolls: Skyrim.
I know, I know. That doesn't make sense right? Well, it does
if you play through it using a bow and arrows, which happens to be my preferred playstyle. I find the combat in Skyrim, and any other Elder Scrolls game for that matter, to be rather bland and dull, with 'click for swing one, or click for swing two' being a rather unintuitive system - But the bow mechanics on the other hand are great! And Skyrim just might have the most satisfying Crossbow gameplay in any game to date.
Of course you can't avoid swinging a sword every now and again - But most FPS games have some kind of melee-element to it.
And just to throw my 2-cents at Mikem: I'd definitely not recommend Plantside 2 to anyone unless they're specifically looking for an MMO. If you're European, you're going to run into a ton of issues just getting the game to run
, and then comes the fact that you're pretty much just a waste of flesh if you're not paying. And then comes the issue that's the main selling point of Planetside 2: 1000 V. 1000 person battles? AZZUM!
And yes.. Yes, in theory! However, 75% of your time will be spent doing skirmishes that involve perhaps 5 people tops, desperately trying to find each other in huge
bases. Not all that entertaining.