My first hatched shiny was a baby Growlithe. I remember being kind of shocked because in all my years playing the games I had never encountered any shiny pokemon before. It was a big moment for me. That was a few years ago. Since then I've also hatched a shiny Froakie and Mismagius.
My first hatched shiny was Venipede. I had shiny Scolipede in my White 2 version and I loved it to bits. But then my sister traded it for loads of legendary pokemons ( which were kinda rare in Gen 5). I missed the beautiful color of shiny Scolipede, so I bred one in my X version.
I have also hatched shiny Vulpix with it's Hidden ability.
Majority of Gen 1 and maybe 15 others spaced around, i'd love to get a complete shiny dex one day, but unfortunately it's impossible, no legitimate way to get Shiny Arceus or a few others.
X/Y onwards gives you a shiny charm to boost shiny rates... shame you need to have seen ALL pokemon beforehand, also the Masuda Method can help with shiny rates, if i remember it's a 1 in 8162 chance to get a shiny, a combination of shiny charm and Masuda brings it down to around 1 in 3500 chance. In other words damn you ish gonna be working lawng and hard, At this point i'm considering just pulling a cheat outta mah butt to turn ALL pokes shiny.
My first hatched shiny was a Shiny Phione. I was bored and decided to mass produce phione for the wonder trade. Then I suddenly got a shiney and was shocked. Then I kept it and then went to breed a shiny bulbasaur.