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 health compared to Warmog's Armor's base amount of 1000 (max 1270).
The 15% damage reduction increased effective health by a raw 15%, providing extremely powerful synergy with health and armor/magic resist. The trifecta of percent damage reduction, resists, and health scales multiplicatively and can be compared analogously to the triple offensive scaling of critical hits, attack damage, and attack speed.
Not including other sources of health or resists, this gave a fully stacked Leviathan an effective health of 943.
As a single purchase without including armor/magic resist, it would require a total of 2180 health for a fully stacked Leviathan to provide an effective health equal to a fully stacked Warmog's Armor (at Warmog's contemporaneous value of 1270 health).
However, with any complementary source of resists, Leviathan easily outscaled Warmog's Armor.
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.