Hit Points
A health system which models the physical health of a character as a number. Taking damage lowers the unit’s hit point total, healing raises it. If hit points reach zero or lower the unit is dead, incapacitated (KO’d), defeated, etc. and can no longer participate in combat.
Prevalence
This may be the single most common mechanic among games that feature some kind of combat. Exceptions are difficult to find in video games, but TTRPGs have some examples (e.g. Mutants and Masterminds).