It is rare to find a fully co-op MMO -- almost every game of this type supports some form of PvP. However, Alex Carobus and I designed Realm of the Mad God to be fully co-op, and I intend for Jetbolt's MMO project to do the same. This is because supporting PvP entails significant costs, and I don't think they're worth paying.
If players are to fight each other, the game's viability teeters on the knife's edge of exact PvP balance. As with the Protoss, Terran and Zerg, any difference in PvP effectiveness between classes spoils the fun. Traditionally, PvP MMO designers have balanced the PvE and PvP games separately. Certain abilities, such as roots, snares and mezzes, have to get nerfed specifically for PvP. Other abilities, such as mind control or charm, make little sense in a PvP context. The result is two different games in one (PvE and PvP), and a serious commitment for thorough, exacting PvP class balance.
Another problem with PvP is griefing. A certain segment of the game-playing population enjoys random ganking, but many are turned off by it. Various games try to control griefing by limiting PvP to certain areas or times. Others rely on reputation systems or NPC guards to keep peace, or they use human gamemasters to adjudicate disputes. In any event, precious developer resources are consumed by the systems that must be built to contain PvP-related griefing.
Supporting PvP also makes the game engine more complicated. Unavoidable Internet lag means that each player sees a slightly different picture of the world. What happens when two players both think they've killed the other? The answer is complicated, and generally unsatisfying to one party or the other.
For all of these reasons, I'm avoiding PvP and building a fully co-op MMO. In addition to simplifying big parts of the game, this decision allows me to focus on deeper co-op gameplay. For example, how can MMO players collaborate to build a city in a way that's satisfying for everyone?