Again, I'm going to cheat and simply reprint a comment I made over at Cameron's site.
First, MMOs attract gamers for more reasons than just the other players. The worlds are huge compared to single-player games, as are loot tables. There's simply more to explore than in single-player games.
That said, the point of playing in the same gameworld as other players can potentially extend far, far beyond grouping. In the real world, individuals constantly affect the lives of others without direct contact. In fact, that's the basis of modern economics. The same can happen in games.
In Shadowbane, I once wandered onto a smoldering ruin. There were no players around, but the burning buildings and broken walls I was viewing were the results of a siege that had taken place just a day or two before I arrived there.
The now extinct Trials of Ascension included many ways in which players could create gameplay for each other without ever meeting. For one example, a player could sacrifice the last of his lives to create a relic which would be randomly hidden in the world.
Simply watching other players run around helps to create the feeling of a living world. Multiplayer can mean so much more than merely grouping!