Well I did know about shinies when I encountered my first (wild one), since a friend of mine had a shiny pichu back then (which in fact turned out to not be that rare in gold and silver, but I digress). I encountered a shiny golbat in the cave prior to the elite four in silver. It learned me a valuable lesson to always stock up on pokeballs... After using my few ultra balls and failing (scared of KOing it) I had no choice but to run away/kill it (I do not know what I did in the end but it does not change the result). I remember being really bummed back then, but knowing how mundane golbats are these days I do not care much about it anymore.
My first actual caught shiny was a shiny spheal in ruby. I remember being extremely happy with it, since I really liked walrein. As such it became my second in command walrein in my team (of course named shiny =p). The other shiny I got in ruby was also due to pure luck, almost even missing it: late at night I was diving under Sootopolis for what I think was some shards for the evolutionary stones (or just a relicanth, I do not know). I was so tired that I did not see the sparkles of a shiny clampearl I encountered. The colours of it aren't that different from the regular sprite, so I barely noticed the difference, capturing it just to be sure. In the end that became my shiny gorrebyss which has completed all of the Hoenn and Sinnoh contests, having over 50 contest ribbons (I should transfer it to the newer games one day).
In Leafgreen I managed to stumble upon a shiny herracross, and again I was extremely excited just running into one.
In Diamond I've gotten a lot of shinies, but through hunting and that did diminish the excitement a lot (using the pokeradar became too easy and more of a chore).
In Hearthgold I stumbled upon a shiny mareep, which I remember made me quite happy (distinctly remember that I made a mistake in a MMORPG that day which nearly made me lose all my ingame currency. This shiny and the fact that my brother managed to correct the mistake really turned the day around), but by then I knew of natures and saw that it wasn't any good.
In Alpha Sapphire my first shiny was an eevee and that really got me to jump in the air from excitement: I was hunting for it using the then still unconfirmed chaining method. Not only that, this was the first pokemon that could be a competitively able pokemon, ending up as my timid 252sp att 252spd Jolteon =)
My second shiny In Alpha Sapphire was a calculated one: I saw some video's on the run away method for hunting shiny latios and specifically got a shiny charm to hunt it. Using a synchronizer, not only did I manage to catch one (in a luxury ball), but also a timid one with 4 maxed IV's. And in the 500 encounters needed I apparently also triggered the 1/20000 chance for pokerus. This has been the most luck I have had to date.
Finally, in pokemon Moon I was just chaining some ditto's for breeding when a blue one appeared out of nowhere. Turns out it has 29/31/31/31/29/31 IV's as well, which did make me quite happy, but considering the rough period I have been going through I think I can not fully comprehend the luck I had here.