I've been incredibly lucky with shinies over the years. I've had five 'full odds' encounters with them, several at the updated Gen 6 half odds, and have intentionally bred/hunted for many more. Granted, I typically play each of these games for hundreds to thousands of hours.
My first (excluding the Red Gyarados) was a Golbat, which I found in the cave connecting Kanto and Johto in original Gold. It immediately became part of my team, and I was able to evolve him into Crobat while battling my way through Kanto, which was pretty cool! I remember being devastated when I realized I wouldn't be able to transfer him to Ruby. ;-;
I also found a shiny Tentacool while surfing in Silver. I wasn't a fan of Tentacool/Tentacruel back then, though (probably because they were so damn common), so didn't even bother evolving it.
Jumping forward several years, and I hatch a shiny Scyther and Staryu while breeding for competitive ones in Diamond. Sadly, and I still regret this...but I ended up giving them away to my best friend. Maybe it was bitterness over losing Crobat, or that I was just super focused on the competitive side of things, but I had zero interest in shinies at that point. My friend actually lost his copy of Pearl not long afterwards too, so it was a complete waste.
A couple of years later, I ran into a Plusle in the National Park in HeartGold. I don't even like Plusle and it's an absolutely terrible shiny, but the unexpectedness of the encounter was really exciting. It made me interested in the idea of shinies again...
So I started looking into how to I could
intentionally get them. I figured out how to do the Masuda Method, and began working on...
Charmander! He was my first Masuda method shiny, and I freaking adored it. Unfortunately, I was young, and figured that my awesome black Charizard should have an equally awesome name. I decided upon ARMAGEDDON. I still have him and cringe every time I see that name, lol. I went on to hatch a shiny Ekans and Electrike in the same way, giving them similarly awful nicknames: BASILISK and INAZUMA.
Moving on to Black version, I got the shiny charm and hatched a Totodile using the MM method. I ended up using him during my playthrough of White 2.
Gen 6 is when things really got out of control. The period of time between finishing the main game of Pokemon Y and Pokemon Bank releasing was so much fun. Nobody was able to transfer their old Pokemon into the game yet, so everybody who cared about competitive play was starting from scratch again. Online trading during this time was on FIRE. I would spend hours each night trading competitively bred Pokemon with people from the old place, reddit, Nuggetbridge and the Smogon forums.
Anyway, somebody asked me to breed them a
female 5IV Charmander, but given the 12.5% chance of females this isn't always an easy task, especially considering you have to get one with the right IV spread, too. I accidentally hatched another shiny Charmander while doing this (granted I was using the MM), and it was
perfect. PERFECT. 31/31/31/31/31/31. Timid, had all the egg moves you'd need. The odds of that must be insane. I used him in most of my online teams during Gen 6.
I went on to hatch many more shinies in Y and Omega Ruby using the Masuda Method, eventually getting the shiny charm as well to increase my chances.
Hatching eggs became something I'd do on autopilot while watching TV, so shinies became inevitable at this stage. It actually got to the point where I sometimes hatched multiple shinies of the same Pokemon so I could get one with the ability I wanted. Froakie for example took five attempts to get one with Protean...
I also found a Scatterbug in Santalune Forest well after beating the game.
And in Omega Ruby I ran into a shiny Taillow on my first visit to Petalburg Woods, and obviously used it in my team for the rest of the game.
Now we're getting into soft-resetting. I had this happen in Omega Ruby:
Didn't have a Master Ball on me, and underestimated how dangerous its' attacks having a combined 20 total PP could be. I put it to sleep repeatedly but it still ran out of moves so quickly, and started struggling itself to death. I started recording that video when I was down to my last attempt at catching it before it knocked itself out.
I learned my lesson from this, and went on to catch Raiou, Latias and Latios in the same way.
I also caught a lot of shiny Pokemon in the Friend Safari, because the odds there (with the shiny charm) were something like 1/500.
And through chain fishing (which also increases your odds substantially), I have caught two Skrelp. Also got another Gligar in a horde.