I really liked the original Crysis. And, even contrary to what seems like the majority of those who finished it (or at least made it that far) I actually liked the zero gravity level (and considering it didn't last that long compared to the rest of the game, there's really nothing to cry about there... and I may have used the word cry on purpose here). I did enjoy it, overall, even though I did think that the A.I. was pretty bad. But it wasn't new to FPS gaming when Crysis was released anyway, bad A.I. in FPS games is an industry standard; with only very few exceptions you can count on one hand, maybe two if you're really pushing it.
I also liked Warhead, it was intelligently connected with the original Crysis. In fact, Warhead often reminds me (conceptually) of Half-Life: Blue Shift. The character of Psycho was well developed, competently voice-acted, and the pace of the game's main events, combined with what I thought to be well-balanced maps (both length and design-wise) all contributed to make a solid FPS experience. I would say that I simply liked Warhead equally to the original, not "better", not "worse, simply just as good.
I've given a try to Crysis 2, with the MALDoHD mod (textures). I made it to... (from memory) what I believe was the 4th map? I'm not sure at this point. Well, suffice it to say that I stopped playing and even surprised myself for not even having the will nor desire to continue. It's been maybe a year now, I think... and I have never touched it again since. I didn't "hate" it. I just didn't find the "fun" (yeah that tends to help to continue on liking AND playing a video game) in it to continue.
I've seen a lot (mostly spoilers-free) of Crysis 3 footage on YouTube for example. Many were video reviews, others were just "let's plays" or demonstrations of maximum in-game settings, etc. From what I have seen it doesn't look like it's a bad game. It's of course visually very detailed... the CryEngine has had nothing to prove to the industry since the original Crysis anyway. But... the thing is I would think that finishing Crysis 2 first before buying Crysis 3 would "help", or maybe it wouldn't. If they made Crysis 3 in the first place is probably because you finish Crysis 2 with a feeling that nothing useful was in fact accomplished. But that's just my guess, I may be wrong and perhaps Crysis 2 "picks itself up" and rises to the occasion at some point in the game. So as far as Crysis 3 goes... I might never know. I really dislike going from point A to point C, without knowing about or getting to point B first in a series or trilogy of games (and no I won't buy Crysis 3 "just because OMG ze graphics!", it'd just take up virtual dust sitting untouched and still uninstalled after purchase in my Origins games library)