I would like to share my insights on Azumarill.
Not too long ago (okay, yesterday), I ran a SubPunch + waterfall and aqua jet on Azu, with an Espeon with Light Screen/Reflect/Work Up/Baton Pass. So firstly I set the screens, do 1 Work Up, then passed to Azu. Then I subbed with Azu and spammed Focus Punch. Turn after turn, my opponent switches between each of his Pokemon which were resistant to the fighting type yet were either built bulky (spatk/atk and hp) or just plain tanky-built sweeper (speed and spatk/atk), and Focus Punch dealt >50% damage. At first I was like, wow this mon can wreck, but then my surprise lessened when I realized the sheer might of Azu's ability. Though this set gets walled by Physically Defensive Unaware Quagsire and Clefable, you can cover up these checks with the right mon in your party.
Anyway, I think Azumarill has S-rank potential. By my observation, the only mons who can suppress and defeat Azu with low risk are Venusaur, Mawile, Breloom and physically defensive unaware mons (as mentioned above), I would mention Pinsir, but without taking significant damage from some sets, Pinsir won't be able to k.o. Azu. Some specific Pokemon can deal with the checks and counters mentioned just recently, notably in my opinion, Mega Charizard Y.
Once set up with Belly Drum, it is a monstrous force to be reckoned with. A simple Aqua Jet will destroy the opposition. Waterfall and Play Rough will crush walls. Knock Off would suppress typical physically defensive tanks which commonly wall Azu, and finally Superpower will just wreck tanky Steel, normal or other types which are otherwise weak to Fighting/resistant to Waterfall. Azu can also excellently run an AV set with it's decent bulk and natural devastating power, or simply be a bulky beast with Choice Band.
To briefly discuss Azu's bulk, she only has 3 weaknesses which other mon in your party can easily be immune/resistant to it, she only takes x1 damage to steel moves, and finally, a 100/80/80 bulk is about the same bulk as of clefable and quagsire, making her bulk already great amongst Pokemon which are built the same as her.