Below I will be explaining the "Tankaiser Carry" my Favorite way to build Mordekaiser.

First, The Anti AP(Ability Power)Carry, I choose 9 Warding for Red and Blue runes with 9 Fortitude for Yellow runes and 3 fortitude Quintessence's. I chose the warding obviously because if I'm aiming for an anti ability power carry I want magic resist. I chose the fortitude Quint's and Yellow's because like it or not Mordekaiser does use health instead of Mana so some health is needed.
Second, The Anti AD(Attack Damage)Carry, I choose 9 Resilience Red and Blue runes with the same fortitude quint's and yellow runes as before in the build above. I chose Resilience obviously because the more armor I have the less attack damage I take.

Anti AP - AD Carry - 0/21/9 - 0/21/9
Breakdown:
I go 21 in Defense for both builds because it gives me everything I want Magic Resist, Armor, Health, some block, and even a little bit of dodge and damage reduction.
I go 9 in Support for the increase HP regen and Exp gain, and the imp. Ghost.

Anti AP Carry -

Doran's Shield

• A good Starter item hp regen with health and armor.
  Mercury Treads
• Boots are pretty much mandatory and these can get u out of some tight spots.
  Force of Nature
• Lovely Item chock full of hp regen with magic resist and Movement speed very nifty early game.
  Sunfire Cape(Depends)
• Lovely item, however only get this item next if your opposing AP team isn't that good, Otherwise might want to go Gaurdian's Angel instead.
  Force of Nature #2
• Yea, I get 2, it's so yummy how much hp regen you get that health really isn't a problem anymore, plus some sick movement speed by this time with some sexy MR(magic resist).
  Gaurdian's Angel
• Wonderful item that enemies usually back away from in-game or avoid a team fight because of this bad boy, I usually get this item after 2nd Force of Nature because by then the enemy usually will be getting stronger as well so this will negate them if they do manage to get you down(which they shouldn't if your playing correctly)so that you can get to safety and regen all that hp back for another round. Also if you got this instead of Sunfire Cape a couple of items up now would be a good time to buy the Sunfire Cape and now is a good time to sell your Doran's Shield to help pay for this item.
  Thornmail
• I know plenty of people have asked me why i have a Thornmail and a Sunfire Cape in my Anti AP build and my answer is the same every time 9 times out of 10 you will never have an entire team composed of all AP Champion's.

Anti AD Carry -

Doran's Shield

• A good Starter item hp regen with health and armor.
  Mercury Treads
• Boots are pretty much mandatory and these can get u out of some tight spots.
  Thornmail
• Yes, Usually rush Thornmail in an AD heavy game simply because its funny to watch them kill themselves.
  Force of Nature
• I will always choose hp regen over health simply because hp regen allows you to get health back during combat and out of combat, where as the more hp you have doesn't matter because once it's gone it's gone. (unless you get healed obviously)
  Gaurdian's Angel
• Wonderful item.
  Force of Nature #2
• More hp regen =)
  Sunfire Cape
• Very nice gives Armor, Health, and does constant damage to surrounding enemies.

Siphon Destruction

1. It has the longest range good for bush checking and it doesn't have a limit on how many creeps it can hit therefore best for your shield.
   Mace of Spades
2. This is probably the most important spell you can use so max it out quickly.
   Creeping Death
3. Not all that important of a spell I spec into it last just because its not that much of a help.
   Children of the Grave
4. The 2nd most important spell in your arsenal this accompanied most of the time by ignite makes you able to successfully Gank, and Solo most champions.(the quick heal is also nifty if u need to escape)

Ghost is extremely useful here because you already have a lot of movement speed from your 2 Force's of Nature, plus it can get you in or out of a team fight quicker.
Ignite is key with Mordekaiser's Ultimate, Children of the Grave, simply because the both do damage over time add them together and it ticks pretty hard.

Normally on 3's map I recommend you solo top so that every now and then you can sneak off to the top jungle and kill creeps get some extra exp and money to get a slight lead on the opposing team.
Normally on a 5's map jungling is a bit harder for two reasons:
1). There is a dedicated jungler on your team.
2). You just don't have time.
In a 5's I recommend jungling whenever you can if your team doesn't have one. This does not mean abandon a tower or a teammate to go jungle, Regardless of how far behind you are in LvL's exp or money. That's just bad team play.

In team fights Mordekaiser can be a big threat or just a wall that gets in the way.
It's important that your team picks a focus so when kaiser ulti smashes that focus with ignite and children of the grave that person dies and you can use his ghost to kill the rest of the team.