Zhong Kui does not come pre-built. Unlike a lot of mages, he needs to adapt to the circumstances to a very large degree. This is an example that's been requested, and I am by no means the foremost Zhong player. Most of the time, you'll want to pick up Sands of Time, but on occasion, Vampiric Shroud will serve you better.
The levelling order is a rough approximation at best. Max your 1, but give your 2 an extra point early on. Always put points in your ult when you can.
Sands of Time
PASSIVE - This item grants 2 MP5 per 10% of your missing Mana
OLD Vampiric Shroud
PASSIVE - Damaging any enemies with an ability gives you bonus 6 health and 3 mana. Can only trigger once per target per ability.
Uncommon Staff
Healing Potion
This consumable heals 250 Health over 25 seconds.
Healing Potion
This consumable heals 250 Health over 25 seconds.
Mana Potion
This consumable heals 150 Mana over 25 seconds.
Mana Potion
This consumable heals 150 Mana over 25 seconds.
Pendulum of Ages
PASSIVE - This item grants 4 MP5 per 10% of your missing Mana. This item grants 7 Magical power per 10% of your available Mana.
Y10 Evolved Warlock's Staff
Evolved Hide of the Urchin
PASSIVE - Provides a Health Shield that gains stacks every 2s. Shield only stacks if you have not taken or dealt damage in the last 5s. Each stack provides 10% of 100 Health +5 Per Level. The full shield will regenerate after 20 seconds.
Void Doumaru
AURA - Enemy gods within 55 units have their Magical Protection reduced by 10%.
Spear of Desolation
PASSIVE - If you receive a kill or assist on an Enemy God all of your non-ultimate cooldowns are reduced by 2 seconds and your ultimate cooldown is reduced by 6 seconds.
Calamitous Rod of Tahuti
PASSIVE - Basic Attacks and Abilities gain 15% additional Magical Power against targets below 60% Health. <n>GLYPH - Successfully hitting an enemy god with an ability calls down a meteor that lands after 1s, dealing 100 (+35% of your Magical Power) damage in a 15 unit radius. This effect can only occur once every 15s.
For defensive builds, Zhong's options are many and varied. I won't list every option, but instead useful items that can fit into builds instead of Hide of the Urchin and Void Stone
Bulwark of Hope
PASSIVE - When you take damage and are below 40% Health, you gain a Shield with health equal to 12% of your Maximum Health for 20s. Can only occur once every 60s.
Pestilence (old)
AURA - Enemy gods within 55 units have their healing reduced by 25%. This does not stack with similar Auras.
Mantle of Discord
PASSIVE - If you take damage below 30% health you unleash a shockwave that stuns all enemies within a range of 20 units for 1s and become immune to Crowd Control for 1s. This effect cannot trigger more than once every 110s.
Breastplate of Determination
GLYPH - Each time you are hit by an ability, gain a stack of 5 Protections that corresponds to the damage type you were hit with, up to a max of 4 of each type. Once you reach max stacks of both kinds, gain a burst of 20% Movement Speed and double your Protections gained by this effect for 8s, after which all stacks are removed.
Jade Emperor's Crown
AURA - Enemy gods within 40 units have their Physical Power reduced by 15%.