I'd say that Mordekaiser is a pretty unique champion, especially his passive.
He does epic damage, great survivability and an awesome ultimate.

You'll need a special "mindset" when playing Mordekaiser - you can't play him as a chicken, because he isn't.. he's a big metal dude with a big metal club.

You often don't run with Mordekaiser, just make sure you get someone with your ultimate (preferably a damage maker, absolutely no tank) and you could easily turn a 1 v 3 situation to a 2 v 2 situation and come out with 3 kills. It might take some time to realize how powerful Mordekaiser really is.

Pros
+ Easy to play
+ Hard to harass
+ Easy to with harass
+ An epic farmer
+ Epic damage
+ AoE abilities & an awesome ultimate
There's just so many cons I could go on for forever..

Cons
- No CC (Rylai's, but that doesn't really count)
- No good initiates
- No escaping abilities (but why would you need that? you're freaking Mordekaiser)

The farming is a very important part of playing Mordekaiser correctly.
If you want to farm properly get early spellvamp!
It's way better then HP Reg and it's a great combo with your passive, as long as you have your minions or (players) you'll be practically impossible to harass.

After the spellvamp you'll need to get some kills and AP stacks, if you aren't getting any kills on your lane your either doing something wrong or your playing against passive long-ranged champions.

Ganking time! (Player farming is extremely important too)
Since Mordekaiser lacks CC or escaping/ganking abilities you'll often need to get some other players to help you with stuns, slows or w/e they can come up with and then it's time for Mordekaiser to shine.

As previously mentioned Mordekaiser lacks any kind of CC / anti-ganking abilities.
Therefor if you get ganked you have 2 choices: ghost away and hope that you'll make it to the nearest turret / player or kill the gankers. Do not underestimate the power and survivability of Mordekaiser, if you do this - you'll fail! Although you'll hopefully realize it after the first game with him.

Just don't forget to place out our Creeping Death (W) on yourself, it gives you magic resist, armor, additional damage and more shield.