I honestly can't choose. I still go back to the multiplayer in all of them. The one i've put the most time into is BO2 though...but I think I just played that because it's easy to get into. They were all great though...except AW for me.
Black Ops III for the specialists and new components such as wall running/swimming while shooting/new game modes. I love playing as the Outrider/Overwatch. Switching the specialists up means the multiplayer never gets boring, as well as the weapon levelling. The last Call of Duty I had prior to this was Ghosts, so excuse me if this sounds very ignorant
CoD4, WaW, MW2, Ghosts, and BO3 are my favorites.
There are different reasons why I like those games. It's hard to get over the fact that CoD4, WaW, and MW2 were my first games, therefore the CoD experience was new and fresh. There weren't any other games in my opinion that could come close to compete with that experience and the community as a whole couldn't get enough..... there was good buzz. I also had friends and family that played whenever they got a chance.
Ghosts and BO3 are a bit different. I really enjoy/enjoyed the gameplay during a time when there was harsh criticism and I myself was suffering from CoD fatigue. These games still offer that FPS smoothness that are the trademark for this franchise. I loved the map design in Ghosts and I really enjoy the movement system in BO3.
Although it's very obvious that the gritty and grimy boots on the ground gameplay that CoD4 and WaW offered made it a great experience and the historical and modern era gameplay appeased to many players. I don't think that is what made it great though. I think it was the relationship between me, the game, and the world around that, that made it special.
This idea will be put to the test come this Nov when Modern Warfare Remastered comes out. Lets see how that multiplayer stands up to the time we are living in now. I'm optimistic and really looking forward to relive great memories and hopefully create new ones, but there is no denying that I'm more excited to play a new game on new maps than playing a game that I already know how to approach.