This is my personal Warwick build. It's not the best out there, but it is pretty good for being able to chase, have your ultimate deal decent damage, and allow you to take down towers and baron with ease. You may wish to swap out the Last whisper for a Black cleaver, or a second Bloodthirster. I personally keep Dorans right through to the end, as it gives a little bonus to armour and life regen, although most games I’m in I don’t get to the last whisper, as the game is normally over before then.
Your Q skill is used for harassing as much as possible, and it is extremely advantageous to get blue buff as much as possible, for the reduced ultimate and Q skill reduction, but mainly for the mana regen effects, as at level 5, your Q skill uses up around 1/7th of total mana, which equates to around 7-8 uses, depending on how often you have to use it.
I level up my Q and E skill as quick as possible, with only 1 level in W until level 13, as it’s not as useful as being able to ‘see’ low health champions anywhere on the Twisted Treeline, and around half of the Summoner’s Rift map. This speed boost allows you to chase people, and hopefully spot the low health champion about to flash over a wall and stun you.
The main Pros are:
-The chasing ability. Warwick is one of, if not THE best chasers in the game. He can also deal the damage at the end, or suppress the champion and allow your team to catch up if you can’t take him on your own.
-The ability to kill towers. Warwick is able to kill towers in seconds, and can push a lane easily. His W skill gives any teammates around him a boost of attack speed as well, which means you and a friendly Master Yi can backdoor a whole life tower if you needed to.
-Solo the Baron. As soon as you have got Starks Fervour and Madreds, and have reached around level 14-16, you can take baron with 1 team mate. Reach level 17/18, or get a stacked Bloodthirster, you can easily solo baron, provided you have blue buff for the spamming of Q and E.
Cons:
-Ignite. Avoid ignite at all costs. It halves your Q skills heal, Halves your passive, and halves your life steal items effectiveness, and deals a small, but annoying amount of damage to you for a small period.
-Stuns. So long as you keep hitting, you stay alive. I was playing against a team with Taric, Twisted Fate, and Amumu recently, and it was stun, stun, stun, and so stopped me hitting them. Stop hitting, you die. Simple as.
-Rammus+Thornmail. This applies to nearly any champion, but if there is an enemy rammus, cry. If he has thornmail as his first item, die a little inside, but stay away from him. A Rammus without thornmail, you can fight and maybe live. A Rammus with Thornmail, 1 vs 1, you are very likely to die.

That’s all I got, I’ll update as new patches come into effect, till then, remember...
‘It’s only fun when they run...’