Back in the days of the NES and SNES, cooperative gameplay was not uncommon. Part of it was certainly the greater influence of arcades back in those years. Cooperative beat-em-ups like Final Fight and Co-op shooters like Contra used to be a staple of arcades. Some arcade games, like the old Simpsons arcade game, supported up to 4 players at once. In those days, the cooperative mode of games was inseparable from the main game mode. In fact, it was often possible for a second player to join a game in the middle of a play session.
Unfortunately, there ha not been very many really good examples of cooperative gameplay being a major selling point of a game ever since the transition to 3D games in the Playstation era. The biggest reason is that 3D games are not well suited to co-op gameplay. In order to have effective co-op gameplay, all of the players need to be able to see their own characters at the same time. This was not a problem in the days of 2D sprite based games, but it is a major problem for 3D games, where having a functioning camera is hard enough when there is only one character. This has led to an unfortunate decline in co-op games over the years. Nowadays, only a handful of games have cooperative play.
There are really only a handful of ways to handle cooperative game in a 3D game. The first and most common method is using split-screen. Unfortunately, splitting the screen in half (or more) severely limits the visual range of the players. It also forces the designers to scrunch the HUD of a game into a smaller area. Larger HDTVs can lessen these problems, but it doesn't change the fact that players will compare the split-screen game to the single-player game experience. Online cooperative gameplay gets around the limitations of split-screen, but it doesn't allow for two people in the same room (such as me and my brother) to enjoy the co-op mode.
In order for a 3D game to have multiple players looking at the same screen at once, there are still a few options. The first option is to use a static camera that looks down on a large area that contains all of the characters. Essentially, a developer has to emulate the effect of a 2D game. Unfortunately, this approach constrains the actions of the players. The characters, as is usually the case in old side-scrolling 2D co-op games, would not have the ability to split up and handle different objectives. Final Fantasy: Crystal Chronicles and the forthcoming Super Smash Bros. Brawl use this approach. The other approach is to use asymmetric characters in the co-op mode. This is done in the N64 game Jet Force Gemini, where one player controlled the main character and his movement, and the other player controlled a floating robot named Floyd that floated next to the main character's head, and could shoot at any target on screen. The recently released Super Mario Galaxy uses a similar mechanic. This solution relegates the second player to a supporting role, but it does have the advantage that the second player can theoretically join in at any time, as was the case in the arcade days.