Shiny-hunting is pretty much all I do in the games anymore. I was really into chaining and MMing for a while, but now I prefer to hunt them at full odds since that eventually started to feel unrewarding. I'm not competitive, so I wouldn't really have anything to keep me playing I didn't Shiny-hunt (though I am getting close to the end of my Shiny wishlist, so I'm not sure what'll keep me playing once I finish that).
The only Shinies I don't really get excited over are repeat Shinies and Shinies of Pokémon that I really dislike (though I try to catch them regardless). And, if I don't already have a team full of Shinies that I like more in that game, I'll absolutely use it on my team!
The Pokémon in my sig are my absolute favorite/most cherished Shinies. Other favorites include a Porygon2 that I accidentally SR'd in Platinum while trying for a Modest nature, a Flareon that I randomly found in X, an Alolan Sandslash that I found by chance shortly after giving up on hatching one, a Misdreavus and Corsola that I found in VC Gold, and a Shedinja from RS that is currently standing in for Mothim in Sword (I've also got a clone of it that follows me around in SoulSilver).
Most of my non-full-odds Shinies hold pretty much no significance to me anymore, though I'm still partial to the Dunsparce I chained in Pearl (even though I found a full-odds one since in VC Gold) and a Glaceon that I MM'd back in Black 2.