It's not usually my style to obsess over a certain game. However...
As people have said, everyones played pokemon nonstop for a good period at some time. I was only ever interested in the single player, because i played the games liek any other RPG. Might have played the series 300 hours total.
Tales of Symphonia as someone else said, i replayed an obscene number of horus into. The highlight of which woudl be beating it over the course of three days. This is an 80 hour game. I've probably played it for 600 total.
Then theres the Touhou series. But unlike most of these other games, playing it for an obscene amount of tiem is the only way to get good. And i certainly have played it a ridiculous amount. Even now theres only a slim chance fo beating Subterranean Animism on Normal mode. It's impossible to estimate how long i've played the series. Lets say 600 hours.
As for these-types-of-games-that-make-the-headlines-in-america-at-least-due-to-claims-alluding-to-a-diagnosed-addiction...You know, guys that spend every waking second on WoW and some ten year olds WoW account gets cancelled and he takes his dads shotgun and kills his whole family. Well i havent played it, but i have played Diablo 2. Got it recently in fact out of nostalgia, as i owned it as a kid. There came a point where i got sick of encountering groups of enemeis that could kill me in three hits, and having to find my corpse, fix my weapons, shell out mroe money to get another mercenary and stock up on potions...every time i died. It probably took about 20 hours to get to that point.