To quest a quest:
One of the staple quest types in EQ2 involves recovering items from areas swarming with enemies. Maybe you have to steal the secret plans from a warlord's camp or grab a box of medicine some gnolls have stolen. The items are physical models on the ground rather than drops from killing creatures and to pick them up you just click on them and wait a few seconds. Being attacked interrupts your attempt to pick up the item so to get at the items you will have to deal with the monsters nearby.
Other quests may require you to kill a named monster but to get to him you have to go through several passageways full of other monsters. The core idea here is pretty solid -- the quest isn't the mundane task of running from A to B or killing some monsters. The quest has another goal entirely and the mundane tasks of travel and killing monsters are challenges to overcome in accomplishing that goal. This disguises what would ordinarily be a grindy kill-list quest, turning it into an adventure where you try to reach the goal as best you can.
Goals and event triggers:
An interesting concept I've seen used with increasing success is the incorporation of ring events and triggers into gameplay. This is where there's a boss creature with good loot but you have to kill his underlings or complete some tasks to make him spawn. For example, there might be a group of cultists worshiping a statue and when you kill the cultists, the statue comes to life. Even though you're killing a dozen monsters, somehow it doesn't feel like a grind. Like with the previous examples, killing the monsters isn't the goal itself but rather a barrier to your goal that must be overcome. This paradigm has been successfully used in a lot of MMO quests to disguise grind -- a good example being escort quests.
In an escort quest you have to lead an NPC to some location as he stumbles through piles of monsters or is attacked periodically. You might have to kill a dozen monsters to keep the escortee safe but somehow it doesn't feel the same as just going out into a field to kill them. Another interesting twist to the formula that I've seen used periodically (though far too infrequently) is to have the player possess and control a monster or another NPC for the duration of a quest. Even though you're still running around killing monsters, the fact you're doing it via another creature with a different skill-set is interesting enough to make it feel new and fresh.
Lazy content development:
Not all ways of covering up grindy gameplay are as effective as those I've described above. Some are an affront to the genre and aren't even successful at disguising the grind. Quests using reams of text to put your actions in a context is possibly the laziest and cheapest thing developers try to give meaning to a grind. I doubt many people would agree that knowing why they're killing 40 goblins in a field is enough to make it feel it isn't a grind.
Similarly, developers have tried adding rewards of faction standings, achievements and even titles for killing a certain number of a type of monster, all in an effort to give meaning to repetitive gameplay. Some add heaps of endgame content as if to say "It's a grind, but it'll be worth it". At its core, though, it doesn't matter if you're doing the same thing over and over again for XP, to reach endgame or to acquire a fancy title at the end of it. If it still feels like a grind, it didn't work.
Repetitive gameplay is an essential part of modern MMOs. It provides us with a linear exchange rate between effort and reward, keeps the learning curve down and ensures we always know what to do in quests. It's the content designer's job to turn that repetitive gameplay into something interesting so that it doesn't feel like a grind. I can't help but feel MMO developers are continually hit-or-miss in that regard and gameplay suffers as a result.