Unique: Drains target champion, dealing 10% of the target's maximum health in physical damage (min. 100) and healing you for the damage dealt. Additionally you steal 25% of their movement speed for 3 seconds - 90 second cooldown. (450 range)
Champions who are highly dependent on basic attacks (Kog'Maw, Jax, Teemo, Tristana, etc.) build this item due to the attack speed, lifesteal, moderate amount of attack damage, and the passive that helps boost their autoattacks. Champions with an attack speed steroids like Graves, Lee Sin, or Nocturne can synergize well with Blade of the Ruined King, making better use of the passive.
Blade of the Ruined King is a great item choice for practically any autoattacking champion that does percent health damage like Kog'Maw and Vayne. It may even be considered for champions that deal percent health damage with an ability like Lee Sin or Nasus.
AD bruisers and assassins often build this item (Talon, Pantheon, Vi, Zed, Kha'Zix, etc.) because its active allows them to effectively chase important targets and deal a reasonable amount of damage.
The passive on-hit damage cannot crit as the bonus damage from the passive is not added onto your auto attack, but considered as bonus on hit effect damage.
The heal from the active effect will not be equal to 15% of the target's health because it is calculated after considering damage mitigation effects.
Randuin's Omen is a strong counter to Blade of the Ruined King, as it provides armor, health, an attack speed slow and a movement speed slow; and the two actives mostly mitigate each other.
Disregarding the active ability and attack speed, to exceed damage gained by The Bloodthirster on a target, the target must have at least (80-25)/(0.08) = 687.5 health. To deal more average damage to a target than a The Bloodthirster from full to no health, the target must have at least 1375 health.
Although Hextech Gunblade and Blade of the Ruined King both have a Bilgewater Cutlass in their recipe, their item actives are considered distinct from one another and will not put each other on cooldown, leading to a considerable degree of slowing if they are used in tandem.
Unique Passive adjusted to "Deals 5% of the target's current Health in bonus physical damage (max 90 damage vs. monsters and minions) on hit.".
Unique Active changed to "Deals 15% of target champion's maximum Health as physical damage (min. 100), heals for the same amount, and steals 30% of the target's Movement Speed for 4 seconds (60 second cooldown)."
Unique Passive: Your attacks deal 4% of the target's current health in magic damage and heals you for half the amount (120 max vs. minions).
Unique Active: Drains target champion, dealing 150 physical damage plus 50% of your attack damage and healing you by the same amount. Additionally, you steal 30% of their movement speed for 2 seconds (1 minute cooldown). (500 range)