I've had a grand total of 7 shinies, the most recent encountered during my Nuzlocke in Ruby right now. Actually, Ruby is the game where I've had the most shinies. Dunno why. I guess it's lucky?
My first was waaaay back in the day, when I had my first ever game: Sapphire. Yeah, I was a latecomer to the PokeGaming world. Anyways, it was my first game, meaning, I was a total amatuer and had NO clue about shinies, so imagine my surprise when I saw a yellow-green Oddish on Route 120. I seriously thought the game was glitched. I was scared, so I ran away and turned off my Sapphire for a while.
I remember looking it up later and after realizing what it was, banged my head on the table. Literally.
My next one was again in Sapphire, an orange Cacnea. This time, I knew what it was immediately and caught it. Cue happy dance.
Third was in Ruby. I was playing my friend's save file and wala, I ran into a mint green Marrill on Route 117! I even remember my friend naming it Minty after it's color. Alas, it was lost after I deleted that save file, forgetting it was there.
Then I found a green Geodude in Firered. I don't remember much about that encounter, but I believe I caught it. I think it was on one of the islands.
Fifth was an orange Poochyena on Route 121 in Emerald. I was so excited, as it was a long time since I'd seen one. I remember I had just spent HOURS looking for a darn Chimecho, so I sent it out to weaken it. I chucked some Ultra Balls at it, but it kept escaping, and then finally it just used Roar on me and fleed. I was in shock for a while after that.
My sixth was just recently in my Nuzlocke on Ruby, where I found a lime green Wingull on one of the ocean routes. I caught it pretty easily. I was super excited, as again, it's been a LONG time since I played my games, and it was nice surprise seeing this little guy.
My seventh I failed to catch, sadly. It was a dark green Zubat, found at Seafloor Cavern, again in Ruby. It was a sad, sad day that day.
I guess I've been pretty lucky to even have SEEN this many shinies, as some people I see have only encountered one. Some peope don't even find them, at least not randomly.