Unique: Your champion gains 32 health per stack, receiving 2 stacks for a kill and 1 stack for an assist. This effect can stack 20 times; you lose a third of your stacks if you die. At 20 stacks, your champion takes 15% less damage.
Even at 20 stacks Leviathan did not give the most health of any item. Leviathan would give 820 HP compared to Warmog's Armor's base amount of 1000.
The 15% damage reduction increased effective health, but not at a fixed amount. The effective health granted by the 15% reduction increased with more armor/magic resist, where 0 armor/magic resist granted 17.6% increase while 100 armor/magic resist granted 35.3% increase. Due to how the damage reduction scaled, it was more efficient on champions with a high health ratings.
Not including base stats, this gave a fully stacked Leviathan an effective health of 965.
As a single purchase without including armor/magic resist, it would take a base health of 1733 for a fully stacked Leviathan to provide an effective health equal to a fully stacked Warmog's Armor (at 1270 health).
Almost all champions would have more than 1733 HP by level 18, meaning the EHP granted by a fully stacked Leviathan was almost always outstrip Warmog's Armor at end game.
The stacking buff granted by Leviathan when a kill or assist was scored was called "Leviathan Armor".
Giant's Belt cost less at 1110g, and provided more health up to 7 stacks.
If one has a Ruby Crystal and the upgrade cost of 800 gold, selling the Ruby Crystal grants a total of 1132 gold: enough to buy a Giant's Belt.
Unique passive: Your champion gains 37.5 health per stack, receiving 2 stacks for a kill or 1 stack for an assist. This effect can stack 20 times; you lose a third of your stacks if you die. At 20 stacks, your champion takes 15% less damage.