This is my current plan for a no-sets Shi Mizu Haori Barbarian. I'm slowly moving towards it with one of my barbs, so I'm sure there's still more optimizations to be done.
You can see all the stats there, but some fun points:
Doesn't have any crit chance on gear
Uses Shi Mizu's Haori for 100% uptime on 100% crit damage
2.1m non-critting sheet damage, 92m toughness, 0 recovery
Combines a very fast attack speed, high fury retention, Whirlwind's Blood Funnel rune (heal for 1% max life with every crit), and a massive health pool (not sure how to find value on d3planner) to stabilize your life at 25% (100% crit chance under 25% means you're healing incredibly fast, 0% crit chance over 25% means you stop healing immediately when you hit the threshold)
Squeezes out extra DPS by using double +35% crit damage + 130% crit damage 1Hs (for a total of +680% crit damage)
Uses Simplicity's Strength (+37% primary skill damage), Depth Diggers (+100% primary skill damage), Bane of the Trapped (+30% damage), Overwhelming Desire (a chance for +35% damage), and Undisputed Champion (Frenzy gains all runes), and +30% Frenzy damage on legs/belt to beef up every hit of Frenzy.
Uses St. Archew's Gage for a temporary absorb shield for an extra several million HP each time you encounter an elite. Should let you feel safer chilling at 25% health.
Irontoe Mudsputters give a ton of uncapped movement speed while at <25% health, Pauldron's of the Skeleton King protects you from an accidental fatal (and returns you to 25% health), Nerves of Steel gives you yet another cheat death (and returns you to 15% health), Esoteric Alternation gives a flat 35% non-Physical damage reduction and +75% to all resistances while below half health, and Relentless reduces the cost of all your skills by 75% and all damage by 50% while below 35% health (see: always).
Skills are all Physical; +60% Physical damage on gear.
With 100% crit chance and insane APS from Frenzy/DW, we also rock 'n roll with WotB giving critical hits a chance to deal 300% weapon damage to all nearby enemies, Battle Rage - Bloodshed giving critical hits a guaranteed 20% damage done to nearby enemies, and a boatload of AoE from Overpower with critical hits having a chance to reduce its cooldown by 1 second.
Snuck in +400% Whirlwind damage ring with an additional +30% from helm/boots
Mortick's Brace gives that lovely +physical and WotB every rune
I'd like to get perma WotB but I'm not entirely sure how. With just Boon of Bul-Kathos and 23.8% CDR I only have 29% WotB uptime. If anyone could weigh in on how to increase that, that'd be awesome.