If you watched any of the NA LCS weekend you saw a lot of Gragas in the jungle. I heard someone describe Gragas as the Lee Sin of the Cinderhulk Meta and that is a fairly apt description.

Abilities

Happy Hour provides him with a high amount of sustain.

Barrel Roll does good damage and applies a significant slow especially if you have time to let it ferment, which allows for some interesting play opportunities.

Body Slam provides excellent mobility as well as a stun.

Drunken Rage provides % health damage, which is good against health stackers and the ability also provides Gragas with a hefty amount of damage reduction.

Explosive Cask good base damage and is an AoE displacement that can be used as an engage or disengage. Caveat is that you can really mess up a team fight with poor placement.

In short the big man has a lot of utility packed into his kit, with good damage, and high mobility, that he can bring to bear early in the game.

Runes and Masteries

I've played around with a few rune and mastery load outs.

14-16-0
9 Magic Pen, 9 Armor, 9 Flat AP, 3 Flat AP Quints

14-16-0
9 Hyd Pen, 9 Armor, 9 Flat AP, 3 Atk Spd Quints

4-26-0 (30% CDR at level 18)
9 Atk Spd, 9 Scaling Health, 9 scaling CDR, 2 Flat + 1 Scaling CDR Quints

And I like the third setup the best for a couple of reasons.

1) Seems a little counter intuitive but his clears are actually more sustained going defensive masteries and CDR.
2) Gragas has trouble with high mobility champions that can dash around. More slows and more body slams help with that.
3) Allows you to mostly skip CDR when considering itemization.
4) It has been my experience that if you have two tanks and one goes deep in the Defense Tree they will be noticeably tankier than one that doesn't

You will notice the lack of armor seals on your first clear, but after that it won't be noticeable.

Gragas can get away without building Armor or MR early due to the damage reduction he gets from Drunken Rage.

Itemization

Obviously situational, but an item path to consider would be as follows

Hunter's Machete, 2x Health Potion, Stealth Ward

Follow-up with

Ranger's Trailblazer + Enchantment: Cinderhulk
Turbo Chemtank
vs AD Thornmail
vs AP Spirit Visage or Locket of the Iron Solari

Righteous Glory helps with engages and all but eliminates Gragas's mana issues, plus provides additional health regeneration, and synergies well with the 25% bonus health provided by Enchantment: Cinderhulk.

Thornmail in conjunction with Gift of the Toadstool does tons of damage to anyone autoattacking you and since you are such a big body, you will draw auto attacks.

Spirit Visage works really well with Happy Hour and the mastery Second Wind and gives you the 10% CDR you need to hit the 40% cap.

Locket is the more team oriented version of Spirit Visage. Get it if your support does not, though strongly encourage your support to get it as Spirit Visage is just flat out better with Gragas's kit.

For boots I would opt into Mercury's Treads, Boots of Swiftness, or Ninja Tabi as the situation warrants. Gragas has enough mobility that Mobility Boots aren't that beneficial.

As far as boots enchantments go, Homeguard, Distortion, or Captain could all be viable choices. Flash engages from Gragas can be devestating if you can catch the right people out of position. E.g. Flash body slam onto the ADC + Explosive Cask to knock them back into your team.

To finish out your build some options would be.

Warmog's Armor - More Health, More Damage, More Healing
Iceborn Gauntlet - for a little AP, AoE slow, and to make your autoattacks really hurt as you will be spamming your spells with 40% CDR

Honorable mention:

Randuin's Omen
Frozen Heart
Banshee's Veil

These are all really good items. Randuin's is first choice for armor as it doesn't put you over the CDR cap and it slows the attacks of anyone targeting you, but here is the thing, with Thornmail and Gift of the Toadstool, you want people to be attacking you. All of the items in this list discourage people from attacking you.

Other Possibilities:

Zz'Rot Portal - kind of feel like this is only a good item if you are ahead or are at least dictating the pace and direction of the game, the later of which is hard in soloqueue. It does offer a healthy amount of both Armor and Magic Resistance which is not something that you usually find in one item.

Tips and Tricks

1) Body Slam can take you through a ton of walls in the game and it allows you to cut some corners that are otherwise impassable.
2) You can cancel the animation for Barrel Roll by casting it mid Body Slam.
3) The hit box on Body Slam is huge, make sure that you have a clear line on anyone that you want to hit with it as a single minion that registers a hit is enough to stop your forward motion.
4) Drunken Rage provides significant damage reduction, make sure to take a swig before diving into a fight and keep it primed while you are siegeing an objective.
5) While taking a swig to fuel Drunken Rage you can't cast your other spells so try not to do that if you are one Body Slam away from your target.

Combos

Body Slam, Barrel Roll, Detonate Barrel, Explosive Cask (Super quick burst)
Drunken Rage, Body Slam, Barrel Roll, Empowered Autoattack, detonate Barrel Roll, Explosive Cask (Mohr burst)
Flash + Body Slam (gives your opponents no time to react)
Flash + Explosive Cask (again, no time to react)

Miscellany
With 40% CDR your Barrel comes off cooldown before the last one has exploded. Need to verify if you can actually cast it again or if you need to wait until the first barrel explodes.