STOP. IF YOU ARE LOOKING FOR A MAJOR PWNAGE BUILD THAT GETS YOU 27-0 STOP HERE. THIS IS A BUILD THAT BENEFITS MAJOR AP TEAMS AND NOT ONE WHERE YOU GO AROUND WRECKING ****. Build is designed for Summoner's Rift. Also, I will note that this is a conditional build. It works against teams with high health that don't put out a lot of damage (Counters against Mundo, Cho'gath, Amumu, etc.) because he will be able to heal back their damage as well as tank and debuff for your team.
Hey everybody. When I saw Release Notes v 118 http://www.leagueoflegends.com/news/release-notes-v100118 I jumped and shouted because of the buff to this build. So, now I must post it so that all can see.

Although I love jungle Warwick with a passion, I must say that Shredwick is very viable with some mana regeneration. As we all know from magewick, Doran's ring can allow any decent warwick to lane (in any lane) and be very destructive.

Pros:

Early Game Kills and more cs lead to more money.
Actually supporting team with debuffs.
Maximum Harassment Early Game leading to minimal enemy cs.

Cons:

Less Jungle Control
No quick dragon
Less Ganks

Marks and Quints of Insight allow for your 3 base items (Wit's End, Madred's Bloodrazors, and Malady) along with Hungering Strike to be of maximum effectiveness.

Seals of Defense make up for your minimal armor and make you more tanky.

Glyphs of Celerity allow for maximum harassment of hungering strike and your Infinite Duress Late Game when you need it.

21 in Offense - This helps with upgraded exhaust, cd reduction, more magic penetration and more overall damage output.
9 in Utility - Upgraded Ghost, faster xp and monetary gain are necessary for quick attainment of level 18 with a nice build to boot.

The items are the foundation of Shredwick. The point of Shredwick is that you get items that proc of your amazing attack speed (Madreds, Wits End, and Malady). These 3 in combination deal significant damage to the enemy (All 3 of these) and even making yourself more tanky (new Wit's End) That all stack with your quick 5 hits from your ultimate.

The boots and the last 2 items are debatable and I recommend for pretty balanced opposing teams and/or teammates.

Boots: Dont get Berserker Greaves because with Hunter's Call you may be exceeding the 2.5 attack speed cap. Other boot options are boots of Swiftness, Sorce Boots, or Boots of Mobility.

Hextech is a good late game grab because it allows for maximum health return while providing more attacking stats.

Frozen Mallet is also a good item because it helps you survive initial damage, before you can heal while slowing the enemy for chasing and providing some additional attack damage.

Some Item builds also good to grab for specific countering outside of 3 main base items:

Casting/CC team:
Definitely Mercury Treads, Get a Banshee's Veil and a Frozen Mallet.

Tanky team:
Sorceror boots, Hextech Gunblade, and a Frozen Mallet.

AD/ Squishy team:
Boots of Mobilty or Swiftness, Bloodthirsters, Infinity Edge.


Edit: Due to revisiting this build and rechecking the math, I have figured that selling Malady for Black Cleaver when you have finished your build will help you more than Malady will.

Another Edit: If you are losing early game and are facing a high burst AP top or any AP for that matter I recommend a Spirit Visage and/or a Banshee's Veil. If you are facing a high damage AD and cannot win lane go for ninja tabi and wriggles lantern into a possible sunfire cape and thornmail

SKILLS



Eternal Thirst - Each of Warwick's attacks will heal him for 6 / 12 / 18 health. Each successive attack against the same target will stack this amount of healing to Warwick up to a maximum of 3 stacks per strike. The stacks remain for 4 seconds.

This is a skill that in combination with Hungering Strike allows Warwick to ignore all harassment and stay focused on minion kills.
TIP: Get 3 hits before triggering Hunter's Call for maximum effectiveness of healing in long team battles or in healing in a creep wave.



Hungering Strike - Takes a bite out of enemy unit for damage and heals Warwick.
Strikes an enemy for the greater value between 75/125/175/225/275 (+1 per ability power) and 8/11/14/17/20% of the target's maximum health (can only do flat damage to monsters), and heals Warwick for 100% of the damage dealt.

Cooldown - 10/9/8/7/6 seconds
Cost - 60/70/80/90/100 Mana
Range - 400

The range on Hungering Strike is essential to his laning/chasing success. Mainly used for restoring life after a quick scuffle, it can also be used to turn around a fight in combination with your ultimate. You maybe have lower damage, lower or 0 lifesteal that time, but with this his damage will be negligible. After maxing out that skill you can use it to get health back after a team fight in the jungle and get back to fight without beeing forced to go to base.
Also abuse this skill early game is always easy with Doran's Ring.



Hunters Call - Warwick lets out a howl, increasing all nearby friendly champions' attack speed for a short time.
Warwick lets out a howl that inspires all nearby allied champions. This increases Warwick's attack speed by 40/50/60/70/80% and all nearby friendly champions' attack speed by half of that for 10 seconds.

Cooldown - 30/27/24/21/18 seconds
Cost - 35 Mana
Range - Self + 1200 AoE

A great AS boost skill that can help your team to bring towers in no time. As you are a proc monster this gives you great synergy later on. For maximum healing, hit 3 times consecutively



Blood Scent - Warwick passively senses weakened enemy champions around him. The scent of blood sends him into a fury causing him to move at incredible speeds.
Warwick senses enemy champions under 50% life within 1500/2300/3100/3900/4700 distance of him; Upon sensing an enemy at low life he will gain 20/25/30/35/40% Movement Speed.

Cooldown - 4 seconds
Cost - No Cost/Toggle
Range - 1500/2300/3100/3900/4700

Blood Scent is a best ingame skill for catching fleeing enemy champs, as well as running away from a loosing battle (if one of their champs have LASTHIT WITH .
If you see option to fast eand easily close the distance to your prey save your Infinite Duress for stopping your prey or to close the distance if that person will use Flash or when you get low on HP, ultimate will heal you quite much thx to the 30% increased lifesteal while performing it.

Infinite Duress - Warwick lunges at an enemy champion, suppressing them for 1.7 seconds. While they are suppressed, Warwick quickly strikes the target 5 times for 33% of his attack damage plus 40 / 60 / 80 extra damage as magic damage, and gains 30% lifesteal.

Cooldown - 90 / 80/ 70 seconds
Cost - 100 / 125 / 150 mana
Range - 700



That said, recommend the following:
Basic Skill Build: Q,W,Q,E,Q,R,Q,W,Q,W,R,W,W,E,E,R,E,E
Explanation with exceptions:
Always level 1 start with Q (except if you are invading for a kill, then the vision of low hp champs will not only help your team but also give u the extra movement speed needed for the kill.)

Second prioritization has a few main factors:
Is your lane opponent faster than you?
Are you winning the lane?
Can you afford to leave your lane to gank?

If you said yes to 2 or more of these questions then max your blood scent over hunter's call. Otherwise max your Hunter's Call before blood scent. (Please note that you should ask these questions every time you choose between these two skills)

And, as with most ultimates, max Infinite Duress at levels 6, 11, and 16.

Flash - Going over walls is essential to a chasing champion that does not have a move that allows him to.
Exhaust - Makes Solo Fights Easier, can save allies, and can make catch-up on chases easier.
OPTIONAL
Instead of Flash
Ghost - Eases Escape and Ganking but you have the extra movement speed from scent so flash is recommended
Cleanse - Warwick can usually run away from most fights as long as one enemy is below half health due to his blood scent. The only exception would be if he is facing heavy crowd control. If you see you are facing a high cc team highly consider this over flash.
Instead of Exhaust
Surge - Great Attacking Summoner Spell, Works Great with ap/as champs.
Ignite - Good against other healing champs and counters enemy soraka healing the champ you are duoing. If they have a soraka or you are facing sion or voilbear definitely get this. If you are facing any other healer the decision is up to you.

Guys after revisiting this build I realize that this build can work anywhere on the map with a few modifications:
For top and mid follow this build
For jungle start with boots and 3 pots then get your dorans rings and continue with the build.

For Support start with Faerie Charm, 2 sight wards, 2 hp pots, and 2 mana pots, then get a philo stone first time back and some more wards, then get boots and dorans rings and more wards, then get merc treads and then wriggles for extra ward, then I would go into your normal build and sell old items to buy new ones only when you need the item spot space.