Morde is a great tanky dps. With a strong build behind him Morde can deal great amounts of AoE damage across many of the opposing team's champions during team fights. I play Morde with tanking in mind. The goal is to have them attack you, but as you have no CC how do you do it? You do it by making them regret leaving you alive. You can quickly dispose of a squishy dps (faster with your teams' help), and through use of your ult gain further dps in the form of a pet. Morde's pet will die if he does, if that isn't enough to get them to attack you then just use it to your advantage and lay into them with everything you've got.

Note: The build name comes from a comment said in game in reference to my old build that made me a bit proud.

Iron Man - This passive gives Morde amazing staying power for pushing and makes him very difficult to kill.

Mace of Spades - Use this ability whenever it's up, it's just added DPS. It can be used to get an extra hit on a fleeing opponent by hitting the nearest minion to them and hoping for it to spread to them.

Creeping Death - Very useful shield and extra DPS. It is my suggestion to place this shield on your 'tank' minion as it goes under an enemy tower to help keep the opponents back from getting the gold or take damage for it. In team fights cast it on whoever is being focused to bolster their damage reduction and deal damage their melee attackers.

Siphon of Destruction - Your bread and butter. This spell is your best way of filling your shield and for harassment. Attempt to have as many targets as possible in this spells AoE each cast, prioritizing champions over minions. You can also use this to determine if someone is in a bush by casting it into the bush while watching your shield, if it goes up someone is in it.

Children of the Grave - The balance shifter. With this ult you can quickly take a team fight from 5v5 to 6v4. Don't forget the health stealing portion of this ability however as it can be used to get you out of a tough situation buying you time to escape. Ranged champions make some of the best pets, but typically whoever is squishiest should be your prime target to quickly shift the numbers of the fight. Whenever using this skill with the intention of netting a kill use ignite first and follow it with this, ignite has a much shorter range and will almost ensure the kill when the opponent is low health.

Cleanse - Morde is very weak against CC, being stunned/silenced/taunted/feared leaves you not only unable to continue dealing damage to your opponnent but also unable to keep your shield fresh allowing them to get into your health. A while placed Cleanse can mean your life in some circumstances. Don't waste cleanse where it isn't really needed however, if the opponent does not have the dps to do any real damage while your CC'd just wait it out unless doing so will lead to a suprised kill while they think your unable to finish them off.

Ignite - A must on Morde, coupled with his ult it will melt most low health champions w/o assistance allowing you to move your focus to another enemy. Once ignite and your ultimate do their work simply send your pet to your next focus and get them down all the quicker.

I use a 9/21/0 build for masteries

Though Mordekaiser is tanky with his shield alone, using defensive masteries makes you quite capable of tanking the opposing team. The spell penetration from the offensive tree is all the assistance you need to deal plenty of damage out to the opposing team.

Greater Mark of Insight x9 (magic penetration)
Greater Seal of Evasion x9 (dodge)
Greater Glyph of Celerity x9 (cool down reduction per level)
Greater Quintessence of Fortitude x3 (flat health)

My item build with Morde has changed a few times over a lot of play time, The following is my current build I use. The one I used before it which is morde tanky though with less damage can be found in the next section.

Starting Item: Doran's Shield (The life and life regeneration makes your use of health to cast less noticable early game) I use this to start in either build

Ionian Boots - Second on the list allowing you to siphon more often keeping your opponent further back in attempt to avoid your harrass. Careful not to spam all your abilities too much to avoid harming yourself too much. If the opposing team is CC heavy you should consider Mercury Treads instead.

Rylai's Crystal Scepter - Third, this item will do a great deal for you. Giving you a larger health pool to utilize your abilities as well as improving there damage and the added slow effect.

Force of Nature - Forth, this item will give you the most MR offered by any single item in the game, and enough health regeneration to leave you worryless in spamming your abilities. You'll find your staying power increases a great deal as well. If you haven't sold your doran shield by now do so, you will no longer be needing it.

Rabadon's Deathcap - Fifth, this item is simply about getting the most out of your abilties. You may wish to push this item before FoN if your having no trouble with your life, it will make you a bigger threat and more likely to be focused on.

Zhonya's Hourglass - Sixth, typically starting with the needlessly large rod unless your taking a lot of physical damage this item works well with Rabadon's and in the case that your being focused a way to keep yourself up a while longer. (You can continue to control your pet while Zhonya's is in effect)

Abyssal scepter - lowering the MR of the opposing team this item helps a good deal with getting the most out of your AoE spells, not to mention increasing the damage output of your allied AP champs. Some might chose to build this in place of FoN in the build order which is fine but the health regen from FoN is very useful. If the team is AP heavy you might also wish to build this item before zhonya's hourglass.

An older build from several patches ago, I attempted to update it some but for the most part its cut and paste from an old guide I was working on.

Doran's Shield - Gives Morde extra staying power to start the game with.

Core Items
Mercury's Treads - Essential item for Morde as CC (stun/fear/silence/taunt) renders him nearly useless

Warmog's Armor - Gives Morde a great deal of health regeneration for all the spells he casts, the extra health doesn't hurt either. It will also improve Force of Nature's passive effect.

Randuin's Omen - The passive and activated abilities of this item are the real reasons you want this item, but the small health and cooldown reduction and armor dont hurt.

Force of Nature - Even more health regeneration for them to have to get through and the MR to cut down that damage. You could substitute another MR item (Abyssal Scepter) if you prefer a little more damage, but the health regeneration is a real beast when they have to get through the shield too.

Attempt to get to at least 800 gold before backing for the first time, picking up Boots of Speed and Regrowth Pendant. If you must back before 800 gold get the boots. Once you have both finish Mercury's Treads then focus on Warmog's Armor. I will typically sell my Doran's Shield around this time to pick up Warden's Mail, then finish Randuin's Omen. Lastly pick up the Force of Nature starting with the Negatron Cloak. From here I typically pick up Zhonya's hourglass then Rabadon's Deathcap to finish my build off.

Situational Items
Rabadon's Deathcap - Maximized damage output allowing you to output considerable damage despite being so tanky.

Zhonya's Hourglass - More damage for your spells meaning more shielding, and the ability to go invulnerable in tight spots.

Lich Bane - Typically coupled with Rabadon's to really bring out the damage of Morde's Mace of spades ability. Yes you lose some value in the worthless mana.

Stark's Fervor - If your team is physical DPS heavy, Stark's is always a way to help your team although not of a great deal of use to yourself.

Aegis of the Legion - If the rest of your team is having survivability issues this is the item, the extra DPS doesn't hurt either.

Abyssal Scepter - If your team is AP heavy this is a good item to have, it can also be used in place of force of nature to get the MR you need, while still providing extra damage to your spells.

Guardian Angel - They're still managing to kill you? Well make um do it twice.

Thorn Mail - Good against physical heavy teams, now you can not only take a beating but they will kill themselves in the attempt.

My builds for Morde tend to be on the expensive side and taking the mid lane really helps get you to where you need to be.

The goal here is not to kill the opponent (if the opportunity presents itself do so), but rather to out level and equip everyone in the game. Using your siphon to harass while farming the minions you should push the opponent back under their turret. At level three you can take a group of wraiths very quickly. Open with siphon then his other two abilities while attacking the main one in the group. Once they are under the tower you should leave the lane quickly and kill their wraiths then your own. When you are comfortable with how far ahead you've gotten (typically post level 6), push the tower they can't stop you now. With the tower broken it is now open season on the other lanes go wreak havoc.

While mid lane, if the opposing champion is playing defensively, dont hesitate to use your ult forcing the enemy to back and improving your staying power via transfer of life, allowing you to more easily break middle tower.

You should be using your siphon to keep your shield up and harass simultaneously as much as possible aiming to either hit all the minions in a wave, some minions and a champion, or both champions. At level 2 stand between the melee and ranged minions with your shield on for easier farming and better position to keep the champions back from the creep waves. Nothing much changes again until you reach level 6.

If you are in a lane with a partner it is best to hold on to your ult until you have a 'certain kill' so as to get the pet and easily push the lane. As a solo you can use your ult to heal up and simultaneously force your opponent into backing, giving you extra staying power and more gold and experience than them.

Initiate team fights as the opposing team will have difficulty killing you, if the team is heavy on CC and you have another on your team who can initiate you may wish to follow them close behind. Once the fight is initiated you should be spamming your abilities on whoever is first on your kill order. If the kill is close use your ultimate. If the enemy team does attempt to focus you down wait it out until your more than half way then use Zhonya's. This will not only confuse the team on what to do for that 2 seconds but will likely get your abilities off their cool down and allow you to bring your shield up quickly. You should be using creeping death on whomever is the opposing teams focus, the extra armor/MR granted by it is a great help. If you are the focus all the better.

As you should already know, you control your pet by alt-right clicking. Your pet is a huge advantage for you. It can be used to deal extra damage to a tower on a push, chase a near dead fleeing enemy through a turret you don't want to risk going through yourself, defend you from attackers while fleeing, or help kill dragon or a buff for you. After a successful group fight you might have a pet but no minion wave near a tower use the pet to tank for your team and increase your odds of getting a tower before the other team recovers. When you send your pet either to tank a tower or to chase and kill an near dead enemy champion it is a good idea to cast creeping death on it to provide that extra bit of dps or armor.

The art of 'running away'. After the odds turn toward the enemy champions you may want to run away. First look to see where your allies are on the map and head that direction if possible (if not head for the closest tower) while pinging yourself to attract attention. Cast your creeping death whenever possible to further reduce the damage you are taking and occasionally stop to hit them with siphon to get your shield up. If you are getting low on health use your ult on one of the pursuers to leech some health. In most cases you should be able to lead them into your team and proceed with wrecking them.

Pros
Passive shield
Lots of AoE damage
Very Useful pet
Uses health to cast

Cons
Very weak aginst strong CC teams
Is looked down on by some high elo players
Has no CC