The problem with Darius is that he crushes anyone who's in melee range. The tradeoff for such dominance is the fact that he's kited to hell with slow base movespeed, no sustain, and no mobility whatsoever. Fixing Darius is much more challenging than a nerf that just ruins any playability whatsoever because he RELIES on being tanky to get any damage dealt in the first place. If his power was shifted from base values to ratios, no one would play him, because he'd have to build glass cannon, and that just isn't viable on any melee without mobility.
Having said all that, he's not overpowered. The lack of mobility is what really kills him, as he's very easily kited, even if he gets Trinity Force or other bonus movespeed. If you play properly, Darius will never get to your carry in teamfights, and he'll be forced to either run at you and die trying to kill your carry, or peel for his carry, a job he does strangely well.
EDIT: My vote goes to Jax as being the most overpowered. His base stats are absolutely retarded high, and he only needs 7k gold to win the game single handedly.