This is how I play Warwick with mainly AD and a bit of armor/magic resist to maximize damage and to overall stay alive. Please note that this build is for people who want to try a different method of playing Warwick or are just tired of jungling. Also keep in mind that this is my FIRST guide om MOBAfire so i'd appreciate some tips.

Pros:
-Great damage
-Fun
-HARD hitting ult
-Reaches full potential of Hunter's Call.


Cons:
-Squishy
-You're probably going to be focused
-You'll be yelled at for not jungling

Laning is easy with Warwick, due to his AMAZING harassing capabilities. Hungering Strike on the champion with the highest HP for maximum heals and use your passive to sustain yourself.
Note that Hungering Strike will DEVOUR your mana and could result in death if misused. Harass only when needed.

I generally get good results with this in normal games, don't try it in ranked games unless you're confident of your abilities and your experience.

My choices:
Exhaust
-Always good for chasing and with the mastery you're able to negate alot of enemy DPS if necessary.

Ghost
I pick this over Flash because it's easier to use and there's no risk of a misclick that can get you killed. It's also easier to pick up the mastery bonus.

Others:
Flash
-Everyone loves this spell and so do I. There's no reason why this wouldn't work.

Ignite
-Hopefully you'll have enough firepower with this build. However, if you want to use it, it makes great harass early game and makes it easy to snatch a first blood.

I don't think runes should matter TOO much. It's really all up to preference.
Some viable runes:
-Armor Pen
-Attack Speed
-Cooldown Reduction
-HP (If you want some survival)
-Magic Pen (For those who love their Q)
-Mana Regen (Helps with Q)

The good thing about Warwick is that he can go for a good while without NEEDING to shop for items. You should be able to get Greaves on your first trip back, start off with a Doran's Ring/Shield depending on your playstyle.

Regarding Madreds: There are people who think it's a waste of money or simply a bad choice on Warwick. I disagree, with the 4% max hp as damage per hit really helps you keep up with your AD or AP carries. It also goes GREAT with Infinite Duress. You COULD skip it and buy something else or just buy Cleaver/Infinity early.

My justification for everything else:
Berserker's Greaves
-You're not going to be tanking and this helps you get some movement speed and proc Madreds in a fight.
Spirit Visage
-A little bit of MR for casters and it helps with Hungering Strike
Black Cleaver
-Your team will be so happy when that Cho'Gath starts losing his armor and his HP starts dropping rapidly, the armor reduction applies for your WHOLE team allowing you to contribute in a teamfight.
Frozen Mallet
-This is only if you find yourself getting focused, you can easily replace this with another item for DPS. However, even if you do decide to buy this you will be contributing by slowing enemies so the rest of your team can attack them.
Infinity Edge
-This is just to seal the deal, so you can TRULY tear that carry you hate a new one.

Not much to be said here. Hunter's Call helps you and your lane partner and is good for getting minion kills, thus making level 2 a bit easier to get to. Hungering Strike is your main source of DPS for a while so that's why you get it ASAP after Hunter's Call. Blood Scent is only picked up when necessary mainly because it's just to make ganking easier, however it's viable to put a point into it at level 4 to assist your teammates in other lanes.

DO NOT INITIATE AS WARWICK!
You have a great skill for it but do NOT use it to initiate, in this build you lack the stamina to survive initiation. Only use your ult whenever you see a target that needs to be stopped for a brief moment of time.
e.g, Fiddlesticks while casting crowstorm.
Try casting Hunter's Call as much as possible, it REALLY does contribute to the total DPS used by your team, it makes the difference between a 6 stack Cho'Gath vs. the Cho'Gath that never got to eat.

Your rotation should consist of:
1. Infinite Duress
2. Hunter's Call
3. Hungering Strike
4. Auto attack
5. Back to step 2 and repeat.

Be sure to jump in AFTER a fight has been initiated, you DON'T want to be the guy that loses ONE teamfight and then shortly after the game.

Thanks for reading :)
To simplify:
-Use Hunter's Call as much as possible
-Use Hungering Strike conservatively or to harass.
-Madreds is able to be switched for another item.
-Most of your DPS will come from Hungering Strike
-DO NOT use Infinite Duress to initiate
-Have fun :)