I have 36! All self-caught, too. Chaining, in case you don't believe me. I feel rather proud. The fact that I got them all myself is even better, as I know that they aren't hacked and more personal too, as I chose their names. ^-^
I had some relative luck on my old Diamond (trainer name Flynn) before the save got corrupted. Managed to catch about five or so (no hacking/RNG chaining required), but none of them had great battle potential (a Quiet Gastly with SpAtk and Spd IV's in the low teens, for example). I know I bartered a few of them for niche Pokémon in my teambuilding scheme. I remember some dude on the GTS rather quickly responded to my shiny offer asking for a Lv100 Pachirisu. (Leftovers and TM26's GALORE!!!)
My current Platinum campaign has no such luck, at the moment. We shall see...
What constitutes as a lot?
I had four I found randomly (drowzee, oddish, zubat, and geodude) but lost the first two in a stupid reset, 3 I got in trades (cleffa, and 2 others...) a few I got from breeding (eevees and magikarp) but about 12 I got using a shiny code
Soooo, around 8 or 9 legit and 12 or so with a code. Alot? Maybe.
Let's see... the Riolu egg I got on Pearl hatched shiny, and I've captured a shiny Kriketune and Shuppet.
Then from the GTS, I've got two shiny Lugia, three shiny Jigglypuff, a shiny Deoxys, Ho-Oh, Charizard, Gyarados, Rayquaza, Pachirisu, Floatzel, Pikachu, Mew, Darkrai, Dialga, Palkia, Regigigas, Seviper, Beedrill, Pichu, and Cresselia. A handful of them are most likely hacked, but most of them look legit.
From friends and people I've traded with on Serebii, there's also a Pidgeot, Shinx, Magneton, and Gastrodon.
Excluding the red Gyarados in Pokemon Crystal I have five:
Politoed (caught as Poliwhirl which I didn't immediately recognise as a shiny)
Machamp (caught as Machamp)
Not many by some people's standards but it considering that I never found any shinies until Pearl it seems enough to me. All were caught in the wild as I've never had either the luck in, or patience to go, chaining for shinies.