How do you counter Mordekaiser?

I realize this question is old, but I feel compelled to add in here.

In addition to what's already been said (boost your MR, don't be afraid to over-nuke him to eat past his shield), there is the topic of range and escape abilities.

Mord is a unique melee in that his abilities have some good AOE and range to them, but he suffers the penalty of normal melee characters in that a good ranged will still be able to keep him at bay. Characters with long range and/or skill shot abilities like Anivia, Ezreal, Kog'maw or Karthus can put pressure on Mord very easily during the laning phase, which is where Mord tends to establish himself. A character with strong lane presence/harassing ability like Nasus, Garen, Vladimir or Fiddlesticks can also hurt Mord's early game by keeping him at the enemy tower where the tower will eat most of the kills.

Mord also suffers from a distinct lack of escape abilities. Ganking Mord can be easy with a properly built tank to bait his abilities into cooldown, and then bum rushing him when he has nothing left with which to counter. Slows and stuns prevent his otherwise relatively high HP and shield from making a difference, so plan ahead.

Mord tends to be very item dependent. A tank Mord ends up having lower overall damage, while a DPS Mord ends up having a very low lifepool and no escape mechanisms. Putting pressure on him in his lane early game prevents him from racking up too much money (which is why he was designed with so much AOE ability), and thus prevents him from getting his really good items at the proper time which would otherwise allow him to become the "powerhouse" that everyone fears.

Don't get me wrong, a properly played Mord is quite good, and a smart player knows how to balance between him being a tank and a burst DPS. But a heavily pressured Mord will crumble late game, and a ganked Mord will have no chance against the proper lineup.

The biggest issue is where you engage him. Iron Man is fine and dandy -- but late game shouldn't be blocking more than a single ability or two -- it's only in the crossfire of a minion wave + team fight that it really shines, simply because Creeping Death, Mace of Spades, and Siphon of Destruction all build up more shield the more units they hit -- whether it be you, your team mates, or your minions.

A) Try to engage Mordekaiser in the bushes or Jungle where your minion wave won't provide additional fuel for his shield.

B) Never engage Mordekaiser solo unless you are a carry or caster-carry, as any properly built tank MK will likely outlast you and win via attrition alone.

C) Get some MR. A tank Mordekaiser will have very little AD, and minimal (if any!) spell penetration. MR reduces the damage from all of his attacks, which means more health for you and less shield for him.

Team Fights

Like with most tanks, just kill everyone else first. If he's built for tanking, he won't be doing much damage and he doesn't have any taunting or interrupting abilities. Once you've taken down their DPS, kill him at your leisure. Even with a full shield he won't hold up long with focused fire from several team mates.

Laning / Solo

Keep an eye on his shield (it shows up under his health bar). If it's more than around 50%, stay away and try to wear him down. Do your damage in bursts, since it doesn't do any good to take his shield down but not follow it up with damage to his health. Don't overestimate his shield -- one or two hits will knock it down, so if he's at half health underneath it he's still vulnerable to a gank.