It is a AS based DPS Kog'maw build.It's my first build by the way.I'm using it for a long time and wanted to share.I will keep it updated and keep improving it with your suggestions.

Since it's an AS based build its really important to start with high AS - Which makes Vampiric Scepter useful.But you can mix it with magic pen. too its up to you...

I'm starting with a Vampiric Scepter so i can stay in the lane as long as i want.
Berserker's Greaves for AS.Phantom Dancer is a need for kog'maw coz he is really slow without it.Bloodthirster for ad/lifesteal.Madred's works great with bio-arcane barrage..
Wriggle's Lantern is important coz it gives you armor with ad and lifesteal and dont forget to use its active.Infinity Edge nothing to explain.....

I'm playing W based.You wont use your abilities much till 6.Just void ooze if needed.Once your ult is on you can start to feast.E-W(while attacking)-Q-R-R-R till the target dies.You can use your Q coz its passive still accepts even its on CD.

*Icathian Surprise - Upon dying, Kog'Maw starts a chain reaction in his body which causes him to move faster and detonate after 4 seconds; dealing 100 + (25 x lvl) true damage to surrounding enemies.

-This allows you to move at an increased speed and then blow up after 4 seconds.Really an awesome passive.It deals true damage and if you can you use it wisely your k/d will never be under 1...

*Caustic Spittle - Passive: Increases Kog'Maw's attack speed. Active: Kog'Maw launches a corrosive projectile which deals magic damage and corrodes the target's armor for 4 seconds.
Passive: Increases Attack Speed by 10/15/20/25/30%.

Active: Kog'Maw launches a corrosive projectile which deals 60/110/160/210/260 (+0.7) magic damage and reduces the target's armor by 5/10/15/20/25.
Cost
60/60/60/60/60 Mana
Range
625
- Passively �±ncreases attack speed which is that build based.And its active grants you armor penetration which is important to take tanks ;)

*Bio-Arcane Barrage -Kog'Maw's attacks gain range and deal a percent of the target's maximum health as magic damage.
Kog'Maw's attacks gain 130/160/190/220/250 range and deal additional magic damage equal to 2/3/4/5/6% (+0.01)% of the target's maximum Health (Max: 100 Damage vs Monsters). Lasts 6 seconds.
Cost
50/50/50/50/50 Mana
Range
530
- You won't use it much at early game.But it will give you your kills at mid-late game.Once you have 2 attack speed %6 of max hp (with madred's %10)and your crazy AD/Crit with an amazing range...They won't have any chance.

*Void Ooze -Kog'Maw launches a peculiar ooze which damages all enemies it passes through and leaves a trail which slows enemies who stand on it.
Kog'Maw launches ooze which deals 60/110/160/210/260 (+0.7) magic damage to enemies it passes through.

Additionally, it leaves a trail which slows enemies by 28/36/44/52/60% for 4 seconds.
Cost
80/90/100/110/120 Mana
Range
1000
- It's your killing tool.First slow them then eat them.you can use it to escape too.

*Living Artillery - Kog'Maw fires a living artillery shell at a great distance dealing damage and revealing targets. Additionally, multiple Living Artilleries in a short period of time cause them to cost additional mana.
Kog'Maw fires artillery from a great distance. After a short delay, the artillery falls dealing 80/120/160 (+0.3) magic damage and reveals targets for 4 seconds (deals 150% bonus damage to Champions).

Each subsequent Living Artillery in the next 6 seconds costs 40/40/40 additional mana (Max 200).
Cost
40/40/40 Mana
- !!! Deals %150 BONUS DAMAGE to champions!!!You slowed them with your e,activated bio-arcane barrage and keep hitting them with your ult too. if they start to run shase them and keep hitting with LA.Dont forget the DELAY!!

Most of you dont use heal,i know.But it really saves your *** even if you get killed you can use it to hurt your killer more and blow him up.
Teleport to get back to lane fast.

Here's some tips
*Don't runaway if you get ganked by 2-3 people coz you cant.Try hit one with lowest hp-defence even you cant kill him you can blow him up(You can use your heal to hurt him much)...
*Stay back in Team fights and try to dont get focused.
*You are good at 1vs1 since you have %43 lifesteal even you die true damage RULEZ.
*Always check the jungle.dont forget to get red buff and of course the money...
*KogMaw is a great Solo Mid Champ. Play it safe, until you get your Ult.Once your ult is on chase them but not too much just keep harassing if they really get close or stay in the lane with low hp e-w(basic attack)-q-r-r-r
Give it a try please and use your ult wisely dont forget the delay.Kog'maws ult is his everything...
*- Revive after death effects don't allow you to use your passive and then revive.

- With Bio-Arcane Barrage your auto-attacks can pass over obstacles, you can also use it with Living Artillery and Void Ooze.

Hope it works for you too...