Not Updated For Current Season
The masteries shown here are not yet updated for the current season, the guide author needs to set up the new masteries. As such, they will be different than the masteries you see in-game.
Why Atk Spd and AP?
Two reasons: First is the synergy between Bio-Arcane Barrage (which gets additional %dmg from AP) and attack speed. Second is Lich's Bane. With the AP you get from Lich's Bane and Rabadon's Deathcap, you deal sizable damage on your next attack following an ability. It is also important to note that all of Kog'Maw's abilities benefit from AP.
This is not the be-all-end-all Kog'Maw spec and is certainly not for everyone. Also, I'm aware that not everyone who reads this is a lvl 30 summoner so you may not have access to all the runes and masteries listed.
While this is a glass cannon spec, it has turned 1v1 ganks around. This being said, laning with someone with Crowd Control will make your life even easier.
I take Greater Mark of Insight (Magic Pen), Greater Seal of Resilience (armor), Great Glyph of Potency (flat AP), and Greater Quintessence of Potency (flat AP). For this build you can change out the Seals to the scaling mp5 or health, Glyphs to scaling AP, and Quintessences can go Magic Pen or Health (for early game survivability).
Aim for 9 points in Offense first before picking up 21 in Utility. While you can go 9/21/0, it's not my preferred style however you can go this route to increase your survivability.
Personally I start with a Long Sword and a Health pot. Reason being is I like to build my Madred's Razor ASAP to help you farm. Also, the passive can proc off neutral monsters as well. As you may have noticed up to this point, your speed is weak so next you'll wanna pick up boots. Now while I have the Berserker's Greaves listed, remember to be flexible. My number two choice is Mercury's Treads. These don't have to be completed immediately. You'll want to start building towards your completed Bloodrazor. Depending on how the match is going, either build Sheen (build into Lich's Bane only after you stack some more AP) or start aiming for Rabadon's Deathcap (soon to be your best friend).
The last two items are going to be completely dependent on how well you've been doing up until this point. If you're having a hard time, Banshee's Veil can be a life saver. Just remember that you can't deal the damage you need if you're dead so play smart. If your team is doing well, grab Nashor's Tooth and Malady. You may also want to switch out Malady for Frozen Mallet for the health and slow. Remember to always weigh your options and adjust your style according to the champs you play against.
When engaging in a fight, Bio-Arcane Barrage is your friend and use Living Artillery to harass.
If you are the "victim" of a potential gank, start with Living Artillery->Bio-Arcane Barrage->Caustic Spittle and send your opponent running and follow them up with a Void Ooze to keep them from living to tell the tale.
I whole heartedly suggest picking up Ghost. You're second Summoner Spell is your personal choice and feel free to move the point placed in Greed into any other Summoner Spell Mastery. I tend to take Ignite.
AP makes Kog'Maw dangerous even when he looks vulnerable. This build will get your Bio-Arcane Barrage up to approximately 10% (plus Madred's Bloodrazor for a total of 14%) and you will be attacking at 2.275 if memory serves which makes most champions drop before they have a chance to react.
Have fun melting faces.