I was thinking about this some more, because I was considering a new MMO that's coming out. I decided not to buy it. It's PvP-based, and even though you can play it for its other elements, that has no appeal for me.
What I would most enjoy (even though it's probably not feasible) is a system whereby you have a co-op area for you and your friends, and then larger public areas. So, depending on the setting:
A pseudo-medieval setting would have hamlets for your co-op group, towns for guilds, and cities and wilderness for everyone.
A modern dystopia might have an apartment building or a trailer for the co-op part, then a larger encampment for guilds, and city ruins for the world at large.
And so on - alien worlds, undersea societies, spaceships, whatever.
Dynamic group events would take place - some challenge to be faced, whether it's a fire or a plague in your hamlet, or a dragon threatening the guild town. As an individual or party, you could also take on quests, but you could also just stay in your hamlet and sandbox away if you like, tending your herbs or blacksmithing.
Leveling would be hidden from the player. I hate leveling! It's unnatural and gets really boring, and I always enjoy my first levels the most anyway. Instead, you would have to seek out someone to teach you a skill, or find a spellbook and actually practice learning a new technique or spell. There would be an alignment system, but it wouldn't necessarily mean that you would have to be the same alignment to get along with an NPC and convince them to teach you. Depending on how you handled the interaction, they might teach you a different spell or skill. If you wanted, you could even concentrate on crafting and become extremely powerful at alchemy, for example. But you wouldn't be able to do ALL the crafts - you'd have to choose. Some of them might go together, like cooking and alchemy, but your skill would have actual meaning based on the time you invested in it. You might need to barter with other players to learn a new recipe or to acquire some material, and they would likewise need things from you that couldn't be acquired out in the world. Let's say I was an enchanter: I could make scrolls to sell, but I could also buy weapons from the blacksmith, enchant them, and re-sell them. The blacksmith would have to buy wood or coal and metals from other players, and they would have to buy axes or picks from the blacksmith.
So it would be a little like a civ game in that a hamlet might have something like wood or metal and the skilled workers to manage and extract it, but they would have to trade with another hamlet for herbs and wool, for instance. A guild might try to convince several hamlets to join them, thereby acquiring friendly traders. But in turn, the guild would risk losing the cooperation of the hamlets if they didn't help out during a crisis.
The people who just love combat could become mercenaries, valued for their unique skills when a monster attacks. Or a nature wizard could be hired to call down rain in the case of a fire or drought.
In short, what I want is the RP that's missing from so many games. I want each player to matter to the world, not just be another stranger running around gobbling up resources and power-leveling. How you interact with other players would be important. If you're a jerk, no one will want to trade with you. If you're helpful and skilled, you could become a sought-after member of the community.