Greetings. I'm building [Kog'maw] as AP and high attack speed. This is a work in progress but I will accept any advice or constructive criticism you may have to offer.

The idea is to have a fast enough attack speed to be the dreaded anti-tank while still being decent at the nuking.

I'm still playing with theses values. Currently I'm running:
[http://www.mobafire.com/league-of-legends/mastery-tree-planner#&tree1=1-0-3-0-4-4-0-0-0-1-3-0-0-4-0-4-1&tree2=0-0-0-0-0-0-0-0-0-0-0-0-0-0-0-0&tree3=1-0-3-0-0-1-0-0-0-0-0-0-0-0-0-0&v=2]

Some of you may be wondering why I didn't go 9/9/9/3 like everyone else. Part of the answer is I have slight OCD and so did the math (including masteries) to make some stats come out to either whole numbers or to a multiple of 5 in the case of cooldown reduction and attack speed.

[http://www.mobafire.com/league-of-legends/rune-page-planner#&rune=351:9-282:9-320:4-303:2-344:3-338:3]

Here's my rune selection breakdown.

Marks

9 Greater Mark of Magic Penetration for 8.55 Magic Penetration

Seals

9 Greater Seal of Attack Speed for 6.84% Attack Speed

Glyphs

4 Greater Glyph of Attack Speed for 2.56% Attack Speed (6.84% + 2.56% + 6% from mastery comes to 15.4%)
2 Greater Glyph of Cooldown Reduction for 1.3% Cooldown Reduction (1.3% + 4% from mastery comes to 5.3%)
3 Greater Glyph of Magic Penetration for 1.71 Magic Penetration (8.55 + 1.71 comes to 10.26)

Quintessence

3 Greater Quintessence of Ability Power for 14.85 Ability Power (14.85 + (4-21) + 5% comes to 19.7925 @ Level 1 and 37.6425 @ Level 18)

My recommended choices are Surge and Flash. Surge provides both AP and Attack Speed while Flash give you an escape mechanic that Kog'Maw sorely lacks.

Ghost, Ignite, and Teleport are all solid alternate choices.

First 3 levels you pick will vary depending on if you're mid or laning with someone. Afterwards, the idea is to level Bio-Arcane Barrage first, then Caustic Spittle for the passive Attack Speed bonus, leaving Void Ooze for last, levelling Living Artillery, like all ults, as soon as able to at levels 6, 11, and 16.

Starting item list will vary by which lane you're starting. If mid, get Doran's Blade for the little Life Steal it gives. If laning with someone, get Boots and 2 Health Potions.

Once you begin the goal will to be to get Berserker's Greaves, Madred's Bloodrazor (favoring Madred's Razors then Recursive Bow), and Nashor's Tooth (favoring Meki Pendant to Fiendish Codex).

The next item I recommend getting is Rylai's Crystal Scepter. Some may argue for Frozen Mallet but there's a reason to go Rylai's. Bio-Arcane Barrage gets an extra 1% for every 100 AP you have. Rylai's gives you lots of AP towards this goal as well as providing some health.

At this point, the game is almost over. If you have time, get Rabadon's Deathcap followed by either Voidstaff if the enemy is stacking Magic Resistance or Zhonya's Hourglass.

One final note: at some point, replace Berserker's Greaves with Sorceror's Shoes. Best time would be after completing Nashor's Tooth as by then, your attack speed will already be quite high.