From Odd Egg in Silver: Igglybuff.
Random encounter: Drowzee.
Truth be told, I was young, so I thought my Igglybuff was sick or something when it hatched :P
I also got a red Magikarp in Emerald, and...
Also on Sapphire, I ran into a shiny Poochyena.....
...The one CHASING Prof. Birch. You know, the one you CAN'T catch?
And also a shiny Ralts on Sapphire. (Level 12 Torchic critical hit, killed it even after being growled at 6 times...) But nothing since Emerald came out, nothing that I caught myself anyway.