Hello ladies and gentlemen! I am PedoBearJK, some may know me, some may not. I've been playing this game since Galio came out, and I just fell in love with the game. (Even after the harsh introduction to the game..) I have around 1300 games under my belt, and of course, Kog Maw was in many of those games.
Free week Kog's always pissed me off because I always thought my build was the only decent way to play Kog Maw, and hence, I make this guide. (Really? Crit Kog Maw?)

Shout out to Extasy771, he's a loser.

When the prophet Malzahar was reborn in Icathia, he was led there by an ominous voice which thereafter anchored itself to his psyche. From within, this voice bestowed upon him terrible purpose, and though Malzahar was no longer tormented by its call, the voice did not cease its unrelenting summons. This baleful beacon's gentle flicker - now fastened to Runeterra - drew forth a putrid beast that ambled across a threshold it did not understand, widening a fissure between spaces which were never meant to meet. There amongst the haunting ruins of Icathia, Kog'Maw manifested in Valoran with unsettling curiosity. The spark which led him to Runeterra teased him still, urging him gently towards Malzahar. It also encouraged him to familiarize himself with his new environment, to the stark horror of everything he encountered on his journey.
The enchanting colors and aromas of Runeterra intoxicated Kog'Maw, and he explored the fruits of the strange world the only way he knew how: by devouring them. At first he sampled only the wild flora and fauna he happened across. As he traversed the parched Tempest Flats, however, he came upon a tribe of nomads. Seemingly unhampered by conventional rules of physics, Kog'Maw consumed every nomad and any obstacles they put in his way, amounting to many times his own mass and volume. The most composed of his victims may have had time to wonder if this was due to the caustic enzymes which stung the ground as they dripped from his gaping mouth, although such musings were abruptly concluded. When his wake of catastrophe reached the Institute of War, an enthusiastic Malzahar greeted him with an enticing prospect: taste the best Runeterra could offer…on the Fields of Justice.

"If that's just hungry, I don't want to see angry."
Tryndamere, the Barbarian King

PROS:

MADE SPECIFICALLY FOR UNITS
HEAVIER THE UNIT, THE BETTER
GOOD FARMER

CONS:

FOCUSED ALOT
CAN'T EFFICIENTLY TAKE OUT TOWERS
RELIANT ON TEAMWORK

Why Rush Madreds?

Madreds is such a good item that syncs with your W really well. It may not allow you to get turrets more efficiently than other items, but it will make you something close to a 'Bionic-Killer.' More health and bulkier it is, the harder it goes down. For example, Mundo's, Super-Minions, Dragon..etc You can eat them for breakfast in less than 20 seconds.

Why Mallet?

Health n Slow. Why not? It's pretty useful since you're not going to rely on your E for slows until late game. Red buff is quite good and also syncs very well with your W, and along with your mallet, well you can pretty much slow errday.

Why Malady?

Reducing your enemies Magic Resist by 24 really isn't bad. Sure you can get other items for magic resist, but you really want that attack speed and that extra 20 magic shredding damage is a plus for your W and Madreds. Remember, bio-killer.

LOL WHY HEXTECH LOL

Wh..Why not? It's got everything in it for you. Ult, E, Q, W, everything! Life steal, spell vamp, attack damage, ability power, and an active slow! Too good to be an item. Nerf it again!
Not going to bother with Guardian Angel. You're bound to get focused with all the damage you're dealing. But, if you're not doing to well and can get a few pokes in without getting hurt, Banshees are always a nice choice.

Ghost/Flash always got me that last few hits I needed or when I need to ***** the f**k out.
However, Exhaust/Ignite/Teleport/Heal is always viable.
*Heal is for when you're at bot lane, WHICH YOU WILL ALWAYS BE AT, (With this build, you're not going to top/jungle/mid) and your support gets Clairvoyance than heal, or does not have a constant heal. (*ie, Janna / Blitz / Leona so on..)