I think the campaign i enjoyed the most for it's story was Black Ops 2. It's probably the only COD game that goes beyond the cliché "bad guys x good american guys". It even has some branching paths and storylines, which was a welcome addition to break the linearity a bit. The villain has a strong personality, he's not just a random terrorist trying to take over the world for no reason, he's a guy you can actually sympathize with. It's a very well written story for a FPS. I'd love to see mature storylines like this one in future CODs. I think Treyarch is doing a much better job for the franchise than Infinity Ward in the last few games. Sure COD reached it's peak with Inifinity Ward (and was created by IW), but after the first MW nothing really good came out from them.
Black Ops 2 also has the best soundtrack of all the COD games. The main theme song was composed by Trent Reznor and it's awesome,
http://www.youtube.com/watch?v=2U9MIKA4uV8 . There's even a song composed by Avenged Sevenfold which is just as great
http://www.youtube.com/watch?v=uJbrTgUL0Dk .
Gameplay wise i think i still prefer the first COD. Multiplayer wise they're all pretty much the same after MW, except for some balance issues here and there and different killstreaks. The one i have played the most in multiplayer was MW3, but i wouldn't call it the best since it has some serious balancing issues (the MP7 being extremely powerful, for example). The first MW for me was the worst, especially with those fucking annoying martyrdom and last stand perks (which later became death streaks instead of perks). Black Ops 1 and 2 are balanced enough in my opinion. Some people hate the progression system in these games, i actually like it. I like getting an incentive for playing and doing well in online games. And i don't think it makes the game unbalanced.