My first shiny was in gold (yes, gold, not HG, a long time ago, I know). It was the first ursaring I encountered, and at first I thought all ursarings were like that. When I began to see others, I realized that mine was the odd one. I thought it was a glitch or something at the time, as I didn't know what a shiny was. It wasn't until gen 3 that I found out what they were, and by that point I'd caught 3 (other than the red gyardos in G, S and C): Ursaring in gold, tentacool in gold, and hoot-hoot in crystal. I still have my ursaring and tentacool, but I lost my hoot-hoot when I reset crystal prior to getting SS and Pl.
The first shiny I encountered in SS was a linoone while working on my pokedex in the safari zone, but sadly it fled on me. I've encountered quite a few others training and wandering since, such as a tentacool, a drowsee, and a pidgeotto, all of which I've caught. They all have average IVs, though, and aren't really usable for much.
In Platinum, I'm only at giratina, trying to catch one with decent IVs and nature (I can't RNG yet), and haven't encountered any shinys.