Does it ever seem strange that all classes complete quests is pretty much the same way? We all kill someone, loot something, and then run back to get a reward. A priest might use a different method to kill a mob than a warrior would, but ultimately both will be killing, probably looting, and then heading back.
It's perhaps asking a bit much to expect every quest to be flexible, but here and there are places where I think Blizzard could add some flavor, make class matter.
Many of the looting quests are for small items: coins or trinkets. Any sensible rogue would see that it's a lot easier, and safer, to sneak in and pickpocket the item rather than cut a path in and back out again. Of course a warrior would opt for the cutting of paths, and by paths I mean people and by people I mean limbs. A sneaky mage might make a very small portal and drop the item somewhere convenient, such as his own bag.
At times we're sent to beat someone up for information. It makes some sense that in general we'd carry out more or less the same brutally physical torture. But why is a warlock or a priest getting his hands dirty with that? Surely fear is a direct path to the outcome of fear. Similarly, mind flay seems like a convenient way to break a mind, through repeated flaying.
Not to leave warriors out of the fun, why is it so often necessary to kill dozens of enemies to drive them away? Surely the exceptionally bloody dissection by axe of a few visible people would help get the point across. Or the sight of the leader screaming in fear could have a similar effect. Turning him into a sheep might not inspire fear, but surely it would cause a bit of disruption in the chain of command, making the remaining enemies less willing to stick around.
This would surely increase replay value as well, making classes play a bit differently, without requiring entirely separate quests for each class. That sounds like a good idea for a company that wants to keep people around.