Mordekaiser is a tanky spellcaster, with a lot of in-lane sustain and power. He is overlooked because he appears to be a complicated champion. A melee mage, with abilities cost health, and has a shield based on damage he deals? He lacks the amazing burst power of an Ahri or a Cassiopeia but he can still win mid or top with good play.
Lategame, he can be a mage who runs in on the front lines, dealing tons of damage and protecting the AD carries so they can do their job. In one 25 minute game, I dealt 77,000 damage and only took 8,000. His shield along with his ult can keep him in teamfights the whole way, even if the team focuses you.
Counter to many annoying mids, such as LeBlanc and Cassiopeia
Able to pave the way in teamfights
Not as powerful as many other mages
Difficult champ to master
No escape mechanism, while you shouldn't really need one
Melee mid, with a mid-ranged poke. Hard to harass long ranged champions Lux, Caitlyn
Runes, masteries, and summoner spells
For my runes, I think defensively with my glyphs and seals, taking flat MR glyphs and armor/lv seals. The reason I take both is that, if you're mid, you're going to be going against an AP champion 95% of the time. You will want the armor benefit once the laning phase is over, and once you hit level 10, the armor/lv is stronger than the flat armor seals. The flat MR will help you from level one, and you will get plenty of magic resistance from a Force of Nature.
I think the same with my masteries. The 9/21/0 gives you a good boost in your abilities, but the defense is even more substantial. including a regrowth pendant, you have +18/5, which will stop you from killing yourself by casting abilities. Any magic pen you can get is also helpful, because you wont match up with the ability power of most people lategame.
Flash is absolutely a must for most champs. It can set you up for a kill, it can get you away from a situation where you can be killed, it can get in the way of Ace in the Hole to potentially save an ally, it's an amazing skill, despite the fact it's nerfed every chance Riot gets.
Between Ignite and Exhaust, it's a toss up. Ignite paired with Children of the Grave can give you enough damage over time to secure a kill, and give you a nice ghost to push a lane or win a teamfight. Exhaust can give you an edge in a 1v1 situation where you need to deal damage more quickly than the other person. Choose whatever fits your personal preference.
I start with a Regrowth Pendant and a red potion. You shouldn't be farming with your abilities all the time, but in a situation where you can get a few minion kills or a harass in with your Siphon of Destruction, you can recover the health cost much faster.
Get your boots and spell vamp quickly, then focus either getting Rylai's Crystal Scepter or Will of the Ancients. If you need another Regrowth Pendant early on, go ahead and get it, it will go into your Force of Nature later on anyway.
The only truly core items for Morde are Rylai's Crystal Scepter and Will of the Ancients. You should build everything else according to how the game is going. Any items like Warmog's Armor, Force of Nature, Thornmail, Rod of Ages, Zhonya's Hourglass, or any other tank/ap items you can think of.
I always have my Siphon of Destruction maxed at 9, and Mace of Spades by 13. Siphon of destruction is a good farming tool, harass, and the best at getting your shield up quickly by casting it at a cluster of minions. Mace of Spades will be your front-line damage in teamfights, and you should cast it every time you can. You should obviously take your Children of the Grave at level 6, 11, and 16.
Usually, you don't draft your mid champion with the first pick, or you can be easily countered. Lots of people feel confident they can win mid with LeBlanc or Twisted Fate, but Mordekaiser can beat them both. The only mids I'd ever be concerned about are Zilean and Yorick, as Yorick can sustain just as well, if not better than Morde, and Zilean can zip in, bomb-rewind-bomb, and zip out. Morde's range cannot compare to either of them. Anyone else who gets close to burst, they will pay dearly for their attempt to kill you.
Always ward when you're going to be pushing against the tower, which you should be doing. If your jungler is going to buy an item like Wriggle's Lantern, ask them to ward the bush thats on the side of the enemy red buff, which is where most ganking comes from. Ward the other bush. 75 gold can potentially be the difference of life and death. If they have a stealth ganker, like Twitch, take a vision ward of course, and if you are crushing mid, there's gold all over the floor, and you are confident you wont die, go for that Oracle's Elixir. If they don't have a jungler/roamer, then save your money.
Let's say you have a team comp of you top, some burst mage mid ( Veigar, in this case) an ad carry, Caitlyn, an off-tank melee bruiser jungler, Jax, and a tank-support, Alistar. You and Alistar should initiate a teamfight, with Jax jumping in quickly. Since you should be doing massive damage after your E and Q, people will turn their attention to you. Suddenly, an Event Horizon appears, and the members of the team who weren't on the edge are going to start backing away from the stun zone. Veigar and Cait come in and start following up with tons of damage, and people are going to back away. Jax should jump and stun someone, and you can hit them with your Children of the Grave. If it's an AD carry, the ghost will come in quite useful. Assuming you killed 3~4 of them, or if you're lucky, aced it, take that ghost and start knocking down towers.
Mordekaiser is a powerful tanky spellcaster, who can initiate teamfights, deal tons of damage, and pave the way to victory. He can counter many people mid and top, and push towers quickly. He can be tricky to learn, but within a few games, you should have a rhythm going. A good Mordekaiser can be an asset to any team!