I've seeI've seen a lot of bad advice regarding Warwick lately. As of patch 6.80, he's been buffed, and should see more play in the near future.

In filthy casuals, which typically run a 2-1-2 setup, Warwick can find a place in a dual-offlane situation. His main problem is that he just doesn't fit well in a full-carry role, nor is he a particularly strong mid, nor can he support very well.

In the pro scene, Warwick's been used a few times as a roamer, and he does decently well in this role, as he has a very good skill-set (chase/stun/damage), and if successful, can transition into a semi-carry.

Edit: Note that in the Pro scene, Warwick is used mainly as an initiator, and needs a skirmisher’s sabre ASAP.

This guide discussed how to pick, build and gear him, and why.

Pros:
+ abilities are well-rounded, useful and easy to use
+ stat growth is good (2.8 / 2.4 / 1.5)
+ his stun still damages through BKB (physical dmg)

Cons:
- ultimate is a single-target debuff that can be purged (BKB/Manta/Diffusal)
- escape skill causes him to take more damage Blood Scent
- difficult to find a place to lane him in competitive LoL

Pick Warwick When:
- You need an initiator and more carry
- You need a carry that peaks a bit earlier than some of the hard carries
- You need a roamer
- You need a tank
- You face low-armor enemies
- You are running an armor-reduction strategy or line-up
- You need a carry for a dual-offlane (2-1-2 setup)
- You intend to get ahead early and snowball with aggression

Do NOT pick Warwick when:
- You don't have any synergy with other physical damage (e.g. no Vayne, Braum)
- The only reason you'd him is to counter an invis/stealth champion
- You need a late-game hard carry
- You need a lane support

I'm not going to go over Warwick's skills in detail, because they aren't that complex. It is, however, worth mentioning that:
Hungering Strike does physical damage, even if the stun is magical
Hunters Call damage counts as damage for Lifesteal auras & items
Hunters Call damage scaling was buffed in patch 6.80 (April 2014)

There's only two real builds for Warwick, although there are minor variants to these two builds:

Build #1
1) Hungering Strike first
2) Early level of Blood Scent for escape / chase
3) Hungering Strike
4) Hunters Call (take a level of it, since you want to max that next)
5) Hungering Strike
6) Infinite Duress (Ult)
7) Hungering Strike
then...
- Max Hunters Call
- Max Blood Scent last

Build #2
1) Hungering Strike first
2) Blood Scent for escape / chase
3) Hungering Strike
4) Blood Scent
5) Hungering Strike
6) Infinite Duress (Ult)
7) Hungering Strike
then...
- Max Blood Scent
- Max Hunters Call last

Why?

Regardless of how you intend to use Warwick, Hungering Strike is his best skill. The stun increases quite a bit as you level it, as does the damage.

Blood Scent is used for chase, and you get to decide whether you need more burst from Hunters Call or more chase from max'ed Blood Scent.

Hunters Call is a fantastic skill, and has recently been buffed in damage, but it's not reliable enough, and Warwickneeds more attack-speed before Hunters Call becomes truly dangerous.

I'm going to make two separate sections for filthy casual items and competitive items, because filthy casuals are so much more flexible.

Aside from the usual Boots and possibly a Wit's End, the first major item a competitive player wants on Warwick is a skirmisher’s sabre.

After that, you're going to work towards a utility item that shuts down the enemy carry, such as a Frozen Mallet, or an item that buffs your team's damage, such as an Wit's End, or you're going to go for a defensive item for your team, like Randuin's Omen.

If all those items are covered or inappropriate, you may end up getting your own Thornmail against a lockdown-heavy team, or you might pick up a Frozen Heart to help with stacking, or even a Randuin's Omen to buff your team.

It is said that it doesn't matter what items you build in a filthy casual, but that said, there are a few items that work better on Warwick than others.

The main "problem" you're trying to solve on Warwick is lack of attack speed. Attack speed gives more Hunters Calles, which gives more damage. Warwick's stats scale quite well, but he could use some hp and mana regen for laning and roaming.

Bloodthirster is a terrific item for Strength carries who want a powerful mid-game boost.

However, you should really offset the hp drain by getting a lifesteal item, such as a Blade of the Ruined King(MoM) or a Frozen Heart(HoD). The MoM isn't that bad a pickup on Warwick, because the extra damage taken from Blood Scent and MoM don't stack. And, even with the increase in damage taken, most championes can't trade hits with Warwickonce you have Infinite Duress up and you're Hunters Calling them in the face.

I'm still testing this theory, but I think Warwick could be a good candidate for a mid champion, using him as a ganker, and then snowballing into an early-peak carry.

I've done well vs. other melee championes as Warwick, because they don't expect the physical damage that Warwick can dish out.

There's been a movement lately to some unusual solo off-laners, such as Shen. Could Warwick be another of those candidates? He's tanky, with high starting EHP, and an escape skill in Blood Scent. Levels are very valuable for him, although he doesn't really have a good way to catch up on farm, unlike Nasus, who can now farm ancients. He also doesn't have a really teamfight-changing ultimate, although an early ultimate on him CAN allow him to get solo pick-offs on supports, or help his team take down tanky championes.

The main problem with Warwick as an off-laner is that he needs a skirmisher’s sabre quickly, so he can initiate, but he won't get much farm as the solo off-laner.

Best Friends:

Warwick's best friends are championes that also have armor reduction, or can buff Warwick's right-click. Volibear] and [[Rengar are two very good lane-mates and teammates for Warwick.

Edit: As pointed out in the comments, any Agility-based right-click carry's damage is buffed greatly by Infinite Duress.

Worst Enemies:

Warwick's worst enemies are those with lockdown that prevent him from repeatedly Hunters Calling enemies in the face ( Kassadin, Morgana and Mordekaiser, or those who go BKB as an early core item, which removes Infinite Duress, such as Anivia, Master Yi or Cho'Gath with his magic immunity.