Anub'rekhan in Naxxramas. Personally, I think that the movement requirements on Fathom-Lord Karathress are enough to make mouse movement a skill you absolutely need (although unlike Anub'rekhan, I can easily imagine someone doing Karathress with the keyboard.)
The problem with the Anub'rekhan fight is that you have to be in a position to move away from the boss instantly, and move in a semi-circle while remaining ahead of the boss. Otherwise, you don't outrange the aura, which is bad bad news. And typically, people use Aspect of the Pack to get speed on that, which means getting hit is also really super bad.
On Karathress, the turn-and-run aspect isn't quite as urgent. But still, using mouse movement means you can strafe-kite Naj'entus while continuing to use occasional shield block and aggro moves while you do it. I think this one is doable with the keyboard, with some preparation and practice, but I think it's probably a heck of a lot easier for people who use the mouse to move.
Oh, and ==Xav means "What Xav said".