Okay, to start of, I have never found a shiny Pokemon before Generation IV. :\ Well, except the Shiny Gyardos and in Shiny Gold (a ROM hack; it was an Ariados), but they don't really count. I've also tried chaining with the Poke Radar and have never caught a shiny by doing that. All the shinies I have caught myself are pure chance, and I've never used an action replay to get a shiny. Anyway...
My first shiny I ever encountered was a Shiny Steelix in Victory Road in Pokemon Diamond. On my first laythrough, I was going through victory Road heading to the Pokemon League, and I find a regular shiny. Since I've played since R/B/Y, I was shocked that a Pokemon that normally requires trading is in the Victory Road, so I tried to catch it. I think I killed it accidentally, so i said to myself "I am going to catch the next Steelix I find." The next Steelix I found was shiny. Since I have never found a shiny (excluding the red Gyardos) before, I freaked out. I remember running straight to my brother, shouting "I found a shiny" really excitedly. It's quite embarassing now that I think about it. Sadly, I lost my Pokemon Diamond cartridge, along with the shiny. It's a shame, because I loved the gold Steelix, and I still hope that I find my Pokemon Diamond again. IIRC, it was male and was un-trained. I'm fairly sure I caught it in a Master Ball.
Several years later, Pokemon Soul Silver and Pokemon Heart Gold are released. I buy them both, which is a first for me. Anyway, I'm playing through Pokemon Soul Silver and I come to Route 38. You know, the route filled with Tauros and I think Magnemite, as well as Meowth (which, IIRC, is exclusive to Soul Silver.) Anyway, I'm going through the route on, you guessed it, my first playthrough and I find a shiny Meowth. Although it's ugly (imo), I caught it anyway because ashiny is a shiny. plus, shiny Persian is pretty cool. I freaked out again when Ii found it. I'm so fail. XD I named it Candy, and I still have it today. It's female and still un-trained, though I want to evolve it into a Persian. It ahs a modest nature and likes to run. Also, I caught it in a Great Ball.
Special mentions go to a shiny Glameow. It's Japanese, and I randomly put a Poliwhirl on the GTS for a Glameow. I think they thought it was holding a Kings Rock. XD Additionally, I got a shiny Charizard over the GTS. There's also the events (Shiny Raikou, Shiny ("Pikachu-coloured") Pichu etc.) and the shiny Gyardos. Additionally, my brother caught a shiny, pink Wooper in the safari zone in Pokemon Platinum.