Hi my name is IamWeedWick and i love the champion Warwick with all of my heart. Thats why it frustrates my to see people build him so wrong. Now you might say well who the F*ck are you, and why does you opinion matter? So if you dont believe me you can just look at my stats. I may not be a great league player but i do know how to play Warwick.
http://na.op.gg/summoner/userName=IamWeedWick

Pros:
+ Great Mid/Late Game
+ Great Early Sustain In Jungle
+ Ult That Suppresses
+ Does Significant Hybrid Damage
+ His E Gives Him Great Mobility

Cons:
- Zero To Little Lane Presence Pre 6
- His Ult Can Be QSS (Quick Silver Sash
- Mana Hungry

Here are my (Recommended) Runes.
Greater Mark Of Attack Damage (+.95 Attack Damage)
Greater Seal Of Armour (+1 Armour)
Greater Glyph of Magic Resist (+1.34 Magic Resist)
Greater Quintessence of Life Steal (+1.5 Lifesteal)

Now you might be like Lifesteal Quints why? Well the answer is they give Warwicks already great sustain a boost and you don't really need the extra AD.

Just Look At The Picture

This Isn't A Static Cookie Cutter Build You will Want To Change The Boots And Sunfire/Randuin Depending on the Enemy Team Comp
Stalker's Blade - Devourer
50 Attack Speed. UNIQUE Passive: Devouring: Deals 25 magic damage on hit. Killing large monsters increases the magic damage of this item by +1. Champion kills or assists increase the magic damage of this item by +2.

UNIQUE Passive: Chilling Smite: Smite can be cast on enemy champions, dealing 28-164 true damage and stealing 20% of the target's movement speed for 2 seconds.

UNIQUE Passive: Jungler: Deal 45 magic damage on hit to monsters over 2 seconds and gain 10 health and 5 mana per second while in combat with monsters. Additionally, you gain 30 gold for every large monster kill.

Get this item the magic damage it does plus the stacking not to mention the CC you get with the Chilling Smite passive.

Mercury's Treads
25 Magic Resistance. UNIQUE Passive: Enhanced Movement: +45 Movement Speed. UNIQUE Passive: Tenacity: The duration of stuns, slows, taunts, fears, silences, blinds and immobilizes are reduced by 35%.

The Tenacity this item gives you is great on Warwick Because it give you great chasing potential and decent MR plus as Warwick you are most likely to get targeted by the enemys CCing abilities. BUT YOU CAN GET NINJA TABI IF THEY HAVE LITTLE TO NO AP AND CROWD CONTROL
Spirit Visage
10 Cooldown Reduction, 400 Health, 55 Magic Resistance. Passive: +100% Base Health Regeneration. UNIQUE Passive: Increases your healing, regeneration and drain effects on yourself by 20%

This item is almost always a must buy (99%). Even if they have no AP this items CDR is very helpful so you can ult quicker for the late game when teamfights happen constantly. Plus the HP regen is great, but by far the most important part is the Increase in self healing this scales with your passive so well that you would be dumb not to get it.

Wit's End
50 Attack Speed, 30 Magic Resistance. UNIQUE Passive: Basic attacks steal 5 Magic Resist from the target (stacks up to 5 times). Basic attacks deal 42 bonus magic damage on hit.

This item is so good on Warwick. Why? you ask, well it scales with your Stalker Blade Devourer. Mixed with Merc Treads it gives you 55 Magic Resistance which is significant, Furthermore it steals the Enemys MR 5 per hit stacking up to 5 times (5x5=25). This is amazing because Believe it or not Warwick does a significant more amour of Magic damage per hit the AD.

Blade of the Ruined King
25 Attack Damage, 40 Attack Speed, 10 Life Steal. UNIQUE Passive: Deals 8% of the target's current Health in bonus physical damage (max 60 damage vs. monsters and minions) on hit. UNIQUE Active: Deals 10% of target champion's maximum Health as physical damage (min. 100), heals for the same amount, and steals 25% of the target's Movement Speed for 3 seconds (90 second cooldown).

Attack Damage, Attack Speed, Life Steal, and a Slow. What is there to not like? Nothing
TL:DR Get this
Sunfire Cape
45 Armor, 450 Health. UNIQUE Passive: Deals 25 + level magic damage per second to nearby enemies.

This is a good item it gives you much needed HP and Armour plus even more magic damage when you're up close to your enemy (Like when you ult them) up to 43 per second. So lets do some math when you ult someone they are suppressed for 1.5 seconds So that a extra 64 magic damage. BUT YOU CAN SWITCH THIS WITH RANDUIN IF YOU WANT THAT EXTRA HP AND ARMOUR AND SLOW ITS UP TO YOU

Eternal Thirst Passive - basic attacks deal additional magic damage and heal you for the same amount, increasing with up to 3 successive striked on same target; it's great ability to help you sustain in jungle and fights and main reason to build attack speed
Hungering Strike Q - short range lock on ability which deals magic damage equal to max 16% of target's max HP or 275 and heals you, stacks with AP; additional damage and sustain ability with high mana cost, usefull when low or fighting 1v1 and finishing chase
Hunters Call W - strong buff with low mana cost increasing your attack speed for max 40% and nearby allies for 20%; can be used often due to its low mana cost to clear jungle, push and buff team in fights, getting assissts
Blood Scent E - toggle on/off ability, reveals enemies below 50% HP in extreme range and significantly buffs your movement speed when active; great for locating isolated vulnerable prey and chasing or retreating from fights, can be turned off to trick victims
Infinite Duress R - high range and mana cost lock on gap-closer, suppressing target for 1.8s striking 5 times dealing magic damage, procing on hit effects with increased lifesteal, stacks with AD; strong CC and only gap-closer, allowing effective ganking and team fighting, damage can be highly increased just by on hit effects.

Warwick is a champion that excels at 1v1s and closing the gap on champions then out trading them with his massive sustain and and deadly mix of Magic Damage and Attack Damage. He should be used late game on successfully ulting the enemy teams ADC or MID or whom ever you perceive as the biggest threat and either killing them or suppressing them so your team can finish them off or run away. But he excels at peeling for your team if you must. But you should be the always one of the first to initiate A teamfight and neutralize A enemy therefore giving your team the edge.