In Torchlight, you can retire a character who has completed the game. Retired characters pass on one item, which gets upgraded stats and lower requirements to equip it, and items can be passed down several times to become ridiculous. Later-generation characters also start with more fame, effectively free skill points. You can also toss your items in the shared stash, but your new level 1 will be a long ways from using that level 50 equipment. (There is also an infinite dungeon for characters who will not be retiring.)
In Kingdom of Loathing, you can ascend with a character who has completed the game. Ascended characters pass on one skill, so players accumulate many skills over time. All non-quest items go into ancestral self-storage, and they can be reclaimed at different times depending on your difficulty setting. Some smaller bonuses also accumulate across the generations or just by merit of having been playing for years. (There is also an infinite dungeon for characters who will not be ascending.)
In Dungeons and Dragons Tiny Adventures (not DDO), any character reaching the level cap automatically retires. Retiring characters pass on one item, which can be equipped at level 1. Many classes, modes, and abilities are opened based on the number of characters retired, no matter what you retire.
What would you think about a MMO that offered something like this? All of the above are single-player games with limited interaction. D&D Online had a steady stream of hate about the design decision to give your first character a lower stat total than later ones, which I think was reversed. This would be more extreme: every successive character receives some improvement. That sounds potentially painful in a game with a level cap and PvP, where being the best would involve having mulched a dozen capped characters already. Balance could be difficult, hitting that window between “not worth it” and “absolutely required,” particularly as the game ages and you need to decide whether the new boss is balanced against newly capped characters or 10th-generation characters.
It could be the worst grind ever. It could also be an exciting way of re-visiting content and mixing the Explorer and Achiever perspectives.
Update: I should note, this is well-worn territory for the MUDers. But the populations, if nothing else, are rather different between MUD grognards and WoW players.