The problem with forcing people to do stuff to progress is that they have to do it to progress. The quests in many games, I prefer to just not do, since either way I am going to end up grinding, but the quests involve a hell of a lot less virtual creatures dieing per second.
Dynamic quests are something I haven't ever seen, and don't think I have ever heard about. Redmoon Online tried this I believe, but never got anywhere on it. Only reason I even knew about it was since there was NPCs randomly with a yellow name. But anyways, an example of a dynamic quest could be that you are just killing monsters in a cave and a little kid runs out with a bunch of monsters chasing him. If you want, you can save the kid, protect him while you lead him out of the cave, then bring him to safety. Or you can have him be a distraction while you pick off the monsters one by one for easier killing.
The advantage over a static quest is that for one, its unique. Who cares about a quest that millions of other players did before, or that you did on your other characters. Also, it introduces a quest in an area you are already in. Power-levelers often choose if a quest is worth it or not by if it can make them earn experience quicker than grinding. But since the quest takes place where you already are, there is no worrying about excessive amounts of boring traveling, or getting pitted against a bunch of weak monsters since you didn't realize the quest existed 30 levels ago.
Unlike static quests, dynamic quests also have the advantage of being much easier to make the world dynamic in result of what you choose to do. After you save the kid, he could just run around town, praising you, until he is stupid enough to run off again. Or if you let him die, his mother could be running around town, asking where her retarded offspring went.
You can even let this go into more quests. Once you bring him out of the cave, you could choose to follow him home, or to let him run home free. Following him home will obvious take you away from your killgasm, but you may have wanted to go to town anyways, or you were getting bored of killing (as blasphemous as that sounds). So you follow him home, take him to his mom, she gives you a little reward. If he didn't get hurt on the way up, the reward could be better for accomplishing a more difficult task. You can then get another quest, from the mom this time, to find materials to make a paddle to beat him since he clearly needs it. Now you are doing a more town-like quest. Being the psychopathic killer you are, you decline, and go back to killing, so the mom goes around town, advertising the need for these quest items. Now someone else has a dynamic quest. To make things more fun, she can even say who brought him back, how long ago, etc.
Now lets say the kid did get hurt on the way up. As you take him back, his mom feels bad since he got hurt, so she wants to heal him instead. Now you are in the same position, but with a slightly crappier reward and you have to get some medical supplies instead. Again, you can do this, or someone else in the game can. And again, if the player declines and another player helps out, the mom and kid can tell the story with the proper names.
So now, we have move on from a retarded NPC who stands at (x,y) and asks for X amount of item I from monster M. Our quest instead involves a random appearance of a town child in any area around the town. You can save him, or not. When you save him, the rewards and following quests involve weather he was hurt or not (could also give better rewards for how quickly you save him, etc). You can continue the quest if you want, or let other people continue it for you. Townsfolk start telling stories about you, and you actually become part of the game.
Damn, that would be sweet. In fact, ignore this post completely - this is what my game's quests are going to be comprised of!