My yearning : A mmo where I can play with friends or other people, where doing something like a dungeon or an instance revolves around more than just getting mobs' hp to 0 over and over. WoW for instance, all the tricks it has is basically boil down to the same dull thing, just varied a bit with the difficulty and the number of mobs.
An ideal is a sort of dungeon/instance with many sorts of perks/tricks for players. Chests is a good example which is already present and is a good one, but other kind of things that may have a short-term bearing on the whole adventure would be fun.
Additionally challenges like Everquest had where you could choose a challenge along the lines of assassinating a boss, collecting a certain amount of items, or rescuing a certain npc. While this was 'marioizing' Everquest, it did sort of have an appeal that with an assortment of other missions that have a little more complexity would be enjoyable to play with some buddies.
Another desirable ideal is being involved in pvp teams versus each other in a Dota like format. When I refer to a Dota like format I'm referring to RoC version.(not the excessively popular Allstars version) Dota's appeal on this format(WC3) was very much on strategy; you're advancing, you select what advancements what may give you an edge at your current level or towards the later objective of sieging the opposing team's base, you select what items you buy choosing what stat to enhance and what items to buy before potentially dieing and losing a certain amount of your gold.
It would be very hard crossing this into mmo territory when you have short-term enhancements, rather than persistent items and fixed abilities instead of developing. But this structure incorporated a little more structure than with say WoW by instead of having 5 people all together, you may have them apart with different objectives but still possessing teamwork. And instead of zerging like battlegrounds where numbers mean everything to who triumphs, you may have a little more structure whereby individual players can have an impact. In Dota, players maybe holding onto a lane, defending their base, sieging, or hero-killing, there was both individual and team importance that could contribute to the outcome of the game.
Didn't want to focus too much on Dota because it does have it's flaws, but it was a very interesting pvp and group structure very different from mmos with their battlegrounds or their 5/6 people grouping together killing perhaps one mob at times.