Today, cooperative multiplayer is just another way of saying you get to play together against a common enemy. This may be an accurate description of a cooperative game from a technical point of view, but as do many modern games, it lacks the spirit that has made past games in the genre so enjoyable. The closest we usually get to cooperative multiplayer any more is in games like Counter-Strike. More simply, this involves two teams of human-controlled characters that battle each other with identical or similar weapons and methods. Almost every game with this competitive team-based multiplayer claims to add some new spin or twist to the usual run-and-gun multiplayer. In my experience, few live up to the task.
Despite the clear convergence to this type of tried-and-true multiplayer gameplay, I believe that there are still many of us that desire the familiar feeling of true cooperative multiplayer. Many of these people are members of massively multiplayer games, where something akin to true cooperative multiplayer still thrives. Those of us who can't spare the monthly subscrpition to these games, though, are left somewhat high and dry, though I would also argue that some MMOs offer only a fraction of the cooperative feeling that is native to the archetype of the genre.
There have been a number of games that I have had the pleasure to partake in that I find to be very enjoyable cooperative experiences. Commandos 2 is probably the leader of the pack, as its entire single-player campaign is nearly flawlessly recreated for multiplayer. What is absolutely essential to the cooperative feeling of a game is codependence. Commandos 2 delivers this in spades since it is extremely difficult to complete the campaign without fairly precise coordination amd cooperation between the players. This is exemplified in the Commandos series in the roles that the players must undertake depending on the characters they control. No one player can do everything, which is a significant element of the formula of codependence.
The critically acclaimed Battlefield games have always prided themselves on the "kit" system and vehicle combat for a rock-paper-scissors feeling that many games have tried to accomplish in place of true cooperative multiplayer. This system encourages and sometimes rewards players for cooperating and working as a unit, though it is infrequent that you'll find a game or server where many of the players will do so. This is mainly due to the fact that while the rock-paper-scissors style does lend itself to cooperative play, the implementation is almost always such that a lone gunman with, enough practice, can be just as deadly as entire squads of less experienced players.
This doesn't mean that cooperative games don't allow players to be more effective or efficient with more experience, because Commandos 2 certainly demonstrates that practice makes perfect, and perfection is satisfying indeed.
An underannounced and underplayed real-time strategy game, Soldiers: Heroes of WWII, takes a page from the Commandos formula, and takes the battle into an entirely 3D environment. On the downside, certain elements of the game make cooperative play more difficult and less entertaining than the Commandos games. The artificial intelligence is my largest gripe with the games, as even though it is a real-time strategy game, success almost unfailingly requires the use of a "direct-control" mode in which you actively command a single unit on the field. This breaks from RTS gameplay more than it does cooperative gameplay, but the mode leaves the game feeling inconsistent with the evident favoritism of the "easier" mode of control.
Games like the Xbox version of Halo allow players to play cooperatively through the single-player campaign, but again, each player is more or less capable of fending for himself, depending on the difficulty of the game and the experience of the player. Multiple players offers more firepower against the enemy and an occasional opportunity to flank the non-player characters, but the player codependence is minimal, and unnecessary at best.
As you may have surmised, codependence is the keystone to good cooperative gameplay, because without it, there is only the player's inclination to cooperate in your efforts, rather than the insistence that you do so. There are definitely other elements that contribute to the feeling of cooperation in a multiplayer game, and in designing the style of future games, I hope that developers will listen to the multitudes of gamers that await the return of true cooperative multiplayer.