Not Updated For Current Season
Warwick is a jungler, and don't believe otherwise. Your main goal with ww is to finish fast. Late in game he's very squishy. In a LATE team fight you can kill one champ and die yourself, because if the other team is any good they will target you among the first. So your optimal game time is 30-35 minutes.
A good heal and damage dealer. Costs a lot of mana.
Your own buff gives you lots of speed. Low mana cost.
They can run but they can't hide.
Your nuke, disables and deals a lot of damage.
Now you may be wondering why I didn't get smite, it's because you don't need it. Some people will say that it makes junling faster, but it doesn't, or at least not that much that you would take it over exhaust and ignite, and when you take smite everyone knows you're jungling.
So why exhaust and ignite. Simple exhaust slows, and in the new patch it weakens the enemy, and ignite gives you extra damage and half's his heal/regeneration.
Now for the runes. WW is all about fast damage and for you to do jungle without smite (and start with blue golem) you need speed.
Mastery's are self explanatory, or so I hope. :)
Now for the start items go with cloth armorand 2 health pots (you only need one but the second is just in case, and you should use it on the red lizard) and the ward that you place in front of baron or dragon so you can see a gank coming ( you should always ask mid to cover his bush because the ward can't cover it).
Now how to jungle. Start with the blue golem, place a ward in front of baron/dragon ( if there are invisible champs on the other team call for backup or wait until you see them in their lanes ). When attacking don't use qstrait off, wait for the golem to hit you twice, use q and then use the first health pot (get him to come into the bush so that there are no nasty surprises, the same for red). When u kill the golem u should be lev 2 take the Hunters Call. Next go for the wolfs use your abilities when ever u can. Then go for the witches. Now u should be lev 3.
Next take on the red lizard (if you didn't get lev 3 kill the small lizards first). And last go for the 2 golems.
Now you should be lev 4 and have the blood scent. At lev 4 you should start ganking. I usually check the lanes and see if someone is having trouble. But if everyone is good you should gank bot/top (the one with 2v2) because you get more kills. When ganking always care about your enemy's health because if he's below 50% your blood scent will trigger and warn him, so turn it on when you want to attack (preferably when you get out of the bush).
When you finish go back to base and shop getand. After that start your.You should jungle once more to get lev 6, and then star to gank actively.
In a team fight always come around the enemy and disable the spell casters with your ulti. NEVER GO IN FIRST. Use wto buff your team mates. Use your ulti wisely don't ulti tanks unles your trying to save someone and watch out fortry using q to disarm it and then use your ulti.
The last two items are changeable but you should always strive for attack damage and attack speed.
So this should pretty much be it, comment if you like it or not and say why.
GG GL HF XD
Side Notes: If they actively harass you in the jungle go and lane they can't harass you forever because they need to level up, get some lev and go strait for the buffs if you think it's safe. I didn't mention dragon because he's pretty much useless now. And as for soloing baron he's been buffed so I don't know if you can now (I'll get back to you on that).