The fact you have to say "I've played a MILLION video games" supports Marilink's theory that you've only played five games.
In many cases a character is immortal but can be temporarily beaten, like Dracula in Castlevania who gets the pulp beaten out of him, but is revived every hundred years, or even Dark Force in Phantasy Star. The Soul Reaver manual says something like "Because you are a vampire, you are immortal. You cannot die." (Soul Reaver has a kind of dying in which you get sent back somewhere in the game, or else that'd be a pretty boring game). And in ActRaiser, you're basically playing as God.

Where are these lemmings going? The
Super Nintendo Super Shire! Hop in line and follow them there!