I’d forgotten about Planescape: Torment and fully agree with its nomination.
It doesn’t help that the plot is complicated enough to confuse adults, never mind kids. You start the game as a heavily scarred and tattooed amnesiac, waking up on a slab in a morgue. You’re in one of the “Outer Planes” of the D&D universe, specifically in the city Sigil on the plane Pandemonium. That’s the easy part.
You keep meeting people who say they know you; many of them hate your guts, some of them join up with you. These probably aren’t mutually exclusive - especially since some of the latter people may not recognize you as you are now.
[spoiler]It turns out that you’re essentially immortal, due to a deal you made with an evil demoness-like being. You do die but come back to life as an amnesiac. Your body also doesn’t get rejuvenated either, so you’re really beat up. It doesn’t help that you get a few opportunities to enhance your powers that also require you mutilate some body part to make it work.
You also know some of your companions, it turns out. One who used to be a man but is now just an animated skull - he was the one who lied to you about how you could be immortal, leading to this twisted existence, and is following you out of guilt. You actually have a tattoo on your back that lists some information for you, which this skull reads off for you. He omits the final line, which warns you to not trust him.
Another, a highly religious warrior, was tricked into following you previously by you giving him forged religious texts that buoyed his spirit when he was doubting his faith. He pledged to follow you always as a result, and not knowing you were immortal, it bound him to you forever. You only saved him because you wanted to get hold of his unique, amazingly powerful sword.
A mad mage who follows you used to be your student. You tormented him and tortured him during his studies, believing he had to suffer fire in order to learn it. It drove him insane, and he tried to burn part of the city down.
And there’s the matter of your former lover, who appears to you as a ghost on and off during the game. In life, she had the gift of prophetic visions, and fell in love with you. You used her for her visions and abandoned her to die when it was convenient for you. Even after that, she still loves you, and you still use her visions. Maybe you even still claim to love her, when you don’t remember her at all.
In one “life” you did things like kill people after learning from them, just to prevent others from learning that information as well. The reason you sought immortality in the first place is because you did so many horrible things in your original life, you knew you could never atone for them all and would be punished in the afterlife. Rather than have the opportunity to try to do so - or at least escape terrible things - your other “selves” have in turn been cold and calculating, or insanely paranoid.
You meet incarnations of your former selves and either defeat them or convince them to join into one being. For the final confrontation, your companions may abandon you, fight at your side, or oppose you. That mad mage that you tortured will not like good behavior from you, for instance. Your last foe is your own mortality, which has gained its own sentience and will, and appears as a man. It has been trying to keep you from finding out about it, as it wants its own life to lead, and has been erasing clues that might lead you to the discovery, and tries to “kill” you when you get close to the secret so you’ll be amnesiac again.[/spoiler]
Add to that the concept of how names have power - claim a false name too often (you don’t know what yours is) and you will make flesh a person by that name who takes offense to your claiming to be him, and that the central question of the story is, “What can change the nature of a man?” and you have a story that is both deeply disturbing and philosophical at the same time.