#2: Drop-in, Drop-out
Look out below!
It may have existed since the dawn of the arcade, but drop-in/drop-out is crucial in today's modern co-op games. Say you see some buddies playing a game, but have a limited amount of time to play with them. Instead of having to interrupt the game in progress, the ability to simply join a game, or leave early without messing the whole thing up, is an important modern convenience.
Why more games don't offer this solution is beyond us, it's quite possibly the most commonly asked question when a new co-op game is announced - "Does it have drop-in/drop-out?" If there's one game that exemplifies this it's Left 4 Dead, not only can you drop-in and out and have a bot take over, you can "step away" and go idle and a bot will pick up your slack.
#1: Online Gameplay
Admit it, you all used AOL at one time in your life.
Many people lead very busy lives, so finding time to actually hang out one-on-one can be difficult. Sometimes jobs or family take us clear across the country, and then what do you do for gaming time with friends? Online co-op was born on PCs in the mid 90's with the advent of many online services, friends now miles apart could game together at the push of a button, no travelling required.
The PS2 generation tried an online system, but without proper voice chat and a standard keyboard, it was a wasted effort. Being able to communicate with teammates to put together strategies is all too important when co-op gaming. Fortunately, this generation utilizes voice chats very well.
This one may not be an obvious “innovation” in the co-op world, but it's certainly one of the most important!
What innovations would you like to have seen on the list? Obviously we can't cover ALL of them.