Unless a game is specifically designed with an eye towards co-op play, it's based on very different rules. Death can't be permanent, but has to have respawn built into it. The game needs to decide if you lose things like keycards, or if one player getting them means that everyone can now open those doors.
Traps have to be designed with a view towards the player coming back after they've been sprung, instead of either getting through/time-travelling to try them again, thanks to the Quickload button. Doom, which let you play through the whole campaign with up to four friends, had it relatively easy. Run round the maze, shoot monsters, move levels.
Even ignoring that the story itself wouldn't work, how would you go about turning Bioshock into a co-op game? What happens if one person triggers a cut-scene, but their partner is hammering the 'skip' button? Even if the mechanics themselves work, players are tough to control.
The original Neverwinter Nights offered a painful campaign if you tried to play it multiplayer. There'd always be someone wanting to hang back and roleplay properly, reading all the text and drinking in the vibe. There'd always be someone who knew where they were going, and would blitz off towards it at lightspeed. Everyone else was trapped in the middle. The campaign could only work if everyone was experiencing it for the first time.
System Shock 2 was much the same. Despite the amount of time Irrational spent trying to bash a fervently single-player game into a multiplayer experience, it simply wasn't fun. Cutscenes, pacing, narrative flow – forget it. What one player will happily accept will quickly have two of them bouncing off the walls.
Back seat questing
Trying to fix these problems led to some interesting solutions – some sensible, some just weird.
No-One Lives Forever 2 offered a dedicated co-op multiplayer mode that took a few of the levels from the regular game, redressing them with new mission objectives that could only be finished as a team.
Zork: Grand Inquisitor was one of the few Myst-style games to be both funny and really enjoyable. Its co-op mode consisted of one person playing the game, and the other acting as a backseat driver to help with puzzles and point out important things.
That was one of the few times such a feature was implemented directly, and for a good reason. Adventures were often played co-operatively, but only when sitting around the same computer. The same technology that enabled co-op play killed any reason to use it, since you could just as easily grab a walkthrough.
The only major online game to even attempt drawing from this well was Uru, the long awaited online edition of Myst. The original release quickly found itself increasingly focused into a single-player game, and not a good one, with its horrible controls and steep system requirements.
The online version came later, and picked up a devoted following, but not enough of one to avoid it being cancelled. Multiple times. It's still running though, as part of the US-based Gametap service.
With all this in mind, you'd be forgiven for thinking that co-op simply fell off the radar. Not so. Ask the 11 million people currently playing World of Warcraft, or the millions more gathering loot in Warhammer, City of Heroes, and other MMORPGs.
While you can 'win' these games (getting to max level) by playing solo, if you want to see the most interesting content, hitting the level cap is just the start of the journey. To see it all, you've got to bring some friends to the party.