What class is the master of escaping arts ?

[Invisibility]

What class is the master to escape dying in encounters in pvp and pve ?

[Triceron]

What class is the master to escape dying in encounters in pvp and pve ?

Not sure if it works today but a nicely timed shadowmeld could be used to reset encounters.

PVE Class-wise, hunters prolly. Feign death worked best. PVP Paladin bubble hearth, unless they nerfed it since I played.

[Calfredd]

Gnomes obviously. Their racial is called Escape Artist after all.

[Nnyco]

Rogue obviously. Vanish+cloak and you gone.

[Ielenia]

Not sure if it works today but a nicely timed shadowmeld could be used to reset encounters.

PVE Class-wise, hunters prolly. Feign death worked best. PVP Paladin bubble hearth, unless they nerfed it since I played.

They did. Buuuut... Dalaran Hearthstone still works since it's a 5-second cast, and pala bubble lasts for 8 seconds.

[Jester Joe]

They did. Buuuut... Dalaran Hearthstone still works since it's a 5-second cast, and pala bubble lasts for 8 seconds.

Divine Shield just flat out reduces the cast time of the normal Hearthstone now. It's baked in but mentioned absolutely nowhere.

[Razion]

Not all immunities or damage reductions are created equal. Sometimes, periodically, immunities and the like will not impact or reduce certain mechanics.

For the purposes of establishing this, the most "get out of jail free cards" are only the passives or actives that literally always prevent death.

Such examples would be:
Cheat Death (Rogue)
Cauterize (Fire Mage)
Ardent Defender (Prot Paladin)
Purgatory (Blood DK)
Last Resort (Vengeance DH)

An ability that does technically prevent death for a while, but doesn't allow one to continue living past the duration is:
Spirit of Redemption (Holy Priest)

Abilities that are quite quite similar to death prevention, but merely activate at low health include:
Nature's Guardian (Shaman)

If we're counting other typical get out of jail free cards (like immunities or 100% of-type DR):
Rogues have two more with Cloak/Evasion (or even, situationally, Vanish)
Mages have Ice Block, and another with Cold Snap after Hypothermia
Paladins have Divine Shield (and can have it again on lower relative CD)
Warriors have Die By the Sword, plus Spell Reflect for a single-targeted spell
Hunters have Aspect of the Turtle (and situationally Feign Death)
DKs can pre-emptively immune magical effects but not direct damage with AMS

And though not damage-prevention in traditional sense, some abilities give a ton of survivability regardless such as:
Metamorphosis (DH)

Overall from counting examples I'd probably say Rogue, with Mage after that, and Paladin after that.

[Powerogue]

night elf rogue. Two vanishes effectively, and cloak of shadows. Very, very, very hard to kill.

[jazen]

druid with aoe roots/improved sprint/prowl.

[muto]

Mage.

2 Cheat Deaths (Cauterize, and Podtender). Ice Block. Alter Time. Invis. 2 Blinks. 2 Frost Novas or 1 + Ring of Frost). Dragons Breath. Polymorph.

Druid would be my second choice, because of being able to shapeshift slows and roots, and cc people with Roots/Cyclone.

[Kuntantee]

If your goal is to just escape, there is only one answer; Rogue. In vertical maps like Revendreth, DH will come close to Rogues.

[Lucavian]

If your goal is to just escape, there is only one answer; Rogue. In vertical maps like Revendreth, DH will come close to Rogues.

Druid. Depending on spec they can shapeshift, stealth, run fast, run even faster, slow fall, lock down targets with roots or ursol's vortex or cyclone. They often even go entire expansions without get nerfed when they should (i.e., bears during legion), thus ESCAPING balance passes.