The GameCube version is my favorite as a game to wake up and play for 30 minutes to an hour before leaving for the day. I have a few moments in it that have stuck to me-- casually talking with Rocko late at night when no one else was awake, listening to my character's echoing footsteps in the lighthouse, being yelled and promptly shot at with a black handgun by one of the snooty villagers. That last one is NOT a joke. I did not make that up.
One thing I like a lot about it is the simplicity; I don't really feel the need to do much to the landscape besides pick weeds and buy flowers to plant now that I've gotten all the trees where I want them. As long as I'm not throwing trash everywhere, the look of the graphics makes it hard for things to feel particularly wrong, I guess. All of it kind of just looks like it's always been there and always will be. I enjoy the lack of options clothing-wise, too-- I don't spend an eternity trying to put together an outfit I like the look of since all you do is choose a single pattern. The silhouettes of the players are set designs that were made very intentionally by the people who designed and modeled them, so they always look very solid to me. I think both of the player models are very cute.
Maybe in part because of the simplicity, there really is a sense of there being mysterious unknowns that can only be speculated upon like Melon might've mentioned. I'll be honest about New Horizons, though.. the characters probably won't admit it, but I'm more than 80% certain there's some freaky cult shit going on in that one. Maybe even PARANORMAL freaky cult shit when it comes to Harv's Island. I swear that dude used some kind of black magic to bring to life a walking, less-than-perfect replica of one of my villagers in his freak shack when I said I wanted to take pictures of them. The Bill that was there probably melted like the guy in Indiana Jones and seeped back into the ground through the floor-boards to Hell when I left to go back to my island.