Black Ops 2 did a rather strange thing with its campaign that no other Call of Duty has, and it's a twist that made it one of my favourite games from the last generation just for the story (that Treyarch multiplayer isn't the only reason I have affection for Blops). Black Ops 2 has a branching plot but not in the normal RPG manner in which the player makes explicit decisions. It's more subtle, and brilliant. Spoilers to follow!
It's possible to play through Black Ops 2 without realising there are meaningful plot branches -- it first hit me when when a friend and I were talking about a mission in which you and the bad guys are racing to find a hacker named Karma. The bad guys get to her first and are running away with her, and if you don't battle through the hordes quickly enough they will get away. There's no countdown clock shown on screen, so it comes off as a standard Call of Duty scenario in which it feels urgent but the outcome is scripted and definite. Whether you save the hacker or the bad guys escape with her maintains that feel; there's no hint that there was an alternative.
At another point, you're tasked with eavesdropping on some bad guys, which involves sneaking around and trying to avoid flying drones while keeping a long-rang mic trained on the target. Regardless of whether you get what you need, the story will continue, with ramifications down the line. There are a number of the possible fail states, and they're integrated so organically; normally games will beat you over the head with plot branches because they really want to make sure you know what it's doing. Black Ops 2 doesn't care about that and it works really well.
There are also several situations in which you have someone's life in your hands and you get to make a choice without really knowing the consequences. In one mission you play as Farid, an American operative working undercover within villain Raul Menendez's terrorist group. Menendez suspects he might be an infiltrator, and hands him a pistol and orders him to shoot another American Operative named Harper. If Farid kills him, his cover stays intact, if he doesn't, then Menedez kills Farid. Later, Menendez and his terrorist army take over a US aircraft carrier and you're briefly given control of Menendez when he confronts American Admiral Briggs -- you can choose to kill or just wound Briggs.
What makes it all work is that these branches function in a direct cause-and-effect way throughout rather than having an underlying system adding up choices and calculating results, like Mass Effect 3's "effective military strength." You need Karma because nobody else will be able to prevent Menendez from escaping imprisonment via cyber-attack in the epilogue. If you rescue and recruit Karma to the cause, but Farid gets himself killed instead of shooting Harper, then Karma will killed on the aircraft carrier because Farid wasn't there to pull the double cross and save her. There are lot of things like that going on in Black Ops 2.
This is a vastly underappreciated way of going about a branching game narrative, and one that works so well with a standard-length 6-7 hour Call of Duty campaign. Playing Black Ops 2 more than once is not a horrifying proposition, as is also the case with Alpha Protocol. It's a shame Black Ops 2 might be the only Call of Duty ever to build a campaign like this.
You can digitally punch the author of this post for giving a shit about story in Call of Duty on Twiitter at @philrowen