From Diablo Wiki
Cooperative play, often referred to as Co-op, is the practice of playing a game together with other humans working towards a common goal.
While Diablo III is not a party-required game, with raid type content that can only be accessed by a group of players working together, the developers clearly intend players to play together, and numerous of Diablo III's systems are designed around co-op play. New features or improvements in Diablo III that are meant to foster more co-op play include:
- Individual item drops. (Players see only the items they can pick up, so no more ninja-looting.)
- No more non-consensual PvP. (No PK switch.)
- No more party system. (Players are automatically in a party together if they are in the same game.)
- Improved Friends List features on Battle.net.
- The Banner system allows players to easily warp to the location of their friends in a game.
- Many quests and boss battles are designed so players can (or must) do them together to receive the rewards.
While these features are definitely boosts to co-op, some fans have pointed out that they're more about the removal of anti-co-op features, rather than the adding of specific benefits to it.
On that side of the coin, Diablo 3 has some areas with fewer co-op bonuses than were present in Diablo 2.
- The maximum players per game has been lowered from 8 to 4.
- The experience gained no longer scales up with more players.
- There are many fewer shared skills in Diablo III. (Many Auras and Warcries shared in Diablo 2, while most Necromancer Curses were of benefit to all characters in the vicinity.)
- The difficulty is so much lower (at least on the beta content) that players have no need to play together in order to succeed.
- The shared stash, shared gold, and shared artisans make self-muling and twinking ridiculously easy, which removes much of the motivation to play with a friend for a rush or to transfer equipment to a new character.
For their part, Blizzard has said little more than, "It's more fun." as an endorsement of why players should team up, rather than playing solo, or going their own way in a larger game. Other than fun, faster killing speed (when in a co-op party) is often brought up as a benefit, as additional players will (theoretically) boost the group's damage output by about 100%, while monsters only gain 75% more hit points in larger games.
Faster killing speed means more drops, more drops means more power or money. Since the goal of the game essentially boils down to either power or wealth, or both, the advantage (in our opinion) is pretty clear and doesn’t need any additional incentive.
Blizzard on Co-Op
While the developers talk constantly about wanting to encourage co-op, they have very little to say in terms of actual benefits or game changes from party play. Faster killing speed from cooperation is just about their only argument. 
- See the Multiplayer article for more details on co-op and related issues.