I haven't found a shiny once (not counting Red Gyrados) and that makes me quite salty. However, if I managed to breed a Timid female Shiny Fennekin, I'm pretty certain that my body would burst into flames from the overwhelming amount of raw hype.
I'll probably do the fishing trick to get a shiny Skrelp or something. Iunno...
I caught a random shiny Spiritomb in the Friend Safari, and it certainly seems people are finding quite a few there. I'd bank on there being some sort of up in the frequency of shiny appearances this gen. It especially feels like it to me since I've never encountered a shiny by chance like that before.
I've played every iteration up until now and have only only ever found three shinies. One was a whismur and the other two were both caterpies. Nothing really interesting, and if I happen to find another in X I imagine it'll be similar.
This guide for catching Shiny Pokemon in X/Y is pretty nice.
I found my first ever Shiny in Sapphire - shiny Tentacool. Green ass motherfucker.
But yeah, I'm 99% sure the shiny rate in X and Y is jacked waaaaay up. My friend who has never had a shiny before got one, and I got another one just out of the blue (he was a blue Electrode actually, dope). I've heard lots of people recounting similar stories.
I weighed in up once, I've got over 600 hours in the main Pokemon games (Red, Yellow, Gold, Diamond, X) ... and I've never caught a shiny except for that red Gyarados. I did contract PokeRus in Gold which had a 3 in 65,536 of ocurring acording to Bulbapedia. Can't win them all.
I did some chain fishing and now possess a shiny Goldeen and Sharpedo. With a pokemon that has Suction Cups or Sticky Hold, it's really hard to not get a bite. I'll have to try radar chaining at some point too, because there aren't a ton of fishing rod pokemon I'd be super stoked to catch.
While I have admittedly ground for nearly 30 hours before the third gym (because... I'm crazy or something), I've found 2 shinies so far just from regular grass; a Skiddo and a Ducklett. I've seen one shiny before that, in Black, which I think was a natural one too. So I'm gonna say shiny rate is up.