Although any origin of "innovation" in MMORPGs is disputed, I believe that it is since World of Warcraft that many MMORPGs use quests to direct the flow of their game, for example to make players explore all corners of a zone, or to get them to the next zone, or even to make them follow the "main" story. This is a very useful trick, which can also be used to great effect for pen & paper roleplaying games. Dungeons & Dragons 4th edition was the first time the word "quest" actually appeared in the index, although of course an NPC sending the group of players on some adventure exists since the earliest pen & paper roleplaying games.

In the specific context of Dungeons & Dragons 4th edition, quests are especially useful. As mentioned before, good tactical encounters for D&D 4E require some preparation, thus being able to steer players into these encounters without having to force them is useful. But they are even more useful if you want to get the game away from just being a series of combat encounters. Exploration and role-playing can always happen, but by using quests and quest rewards the DM can overcome the problem of players preferring combat just because that is where the rewards are. An adventure that has a couple of quests which require non-combat activities from the players helps a lot to break up the perception of 4E as being just about combat.

I find it very useful to create quest handouts for my campaign, stating the goal, quest level and xp reward, and whether it is a major or minor quest. I don't use the MMORPG convention that a quest always starts with an NPC and that you need to return to that NPC to get your reward. If the players hear of some evil afoot, that is enough for them to get the quest. The added value of the handouts is that due to us playing only every other week, it is useful to have a goal written down somewhere. You'd be surprised how much one can forget between play sessions.

Of course there are other solutions for these problems. But I find that these quests fit in very well with the very rules-centric 4th edition of Dungeons & Dragons. They would probably fit less well in systems where there are few rules and the DM makes up everything as rulings on the spot.