this is almost better suited for the "changes in game mechanics" topic, but I'll jot down a few thoughts in this thread instead:
The examples I list are not necessarily "the first" instances, but rather what springs to my mind. Before the internet days, multi player first happened on the same computer. Either you were acting on the same screen (save new york) or one after the other (hot seat mode in Empire), or even with split screens (battle isle).
It was quite a revelation when two computers were hooked up and each player had their own screen (populous) and then the LAN sessions of games like warcraft started and finally internet multi player became the norm.
However, most of those multi player experiences were confrontational. Lately, the single player story mode was made available as multi player co-op in games. Although Transformers War for Cybertron tried a three player co-op mode, I feel that two player co-op mode is indeed the best option, as A) the more people you have, the more difficult it gets to find a suitable time slot to play and B) I have the impression that there are more couples playing games these days, so multi player co-op would be ideal for them.
All the best,