The first shiny that I ever caught, not just R/S/E, was a shiny Shroomish in the Petalburg Woods. I don't even remember doing it, but years later, I found it sitting in my PC right before I was planning to restart my game. I ended up trading it to my Fire Red, and later my HeartGold, where it is currently a Breloom.
The other shiny Pokemon I caught in Sapphire was a Heracross in the Safari Zone. I had back luck with a shiny Paras in the Fire Red Safari Zone, so I wasn't about to let this Heracross go. I threw about 3 or 4 Pokeblocks at it before using Safari Balls, and on about the sixth try, I caught it. It was also migrated to my HeartGold, where it is one of my most powerful Pokemon right now.