Hmm, the shinies that I can remember off of the top of my head (so, not including things like that vaguely remembered shiny tentacool)...
Mostly an UTTER PAIN...
Pokemon Emerald, heading up to fight my rival for the first time, I ran into a shiny poochyena. Obviously, I couldn't catch it, as you don't GET pokeballs until AFTER your rival fight #1... T`_T
Pokemon Diamond, I was training in the area where you first get your starter and ran into a shiny starly. Cue swearing as at that point: a) Otoojio (my now-empoleon) would KO it in a single hit with ANY of his moves (he was a prinplup at that point, and it was level 2 or 3...), b) I had not yet, again, obtained pokeballs. ...
... TT`_TT
But whatever, If I HAD caught it, I would never have gotten Miru, so I don't complain, merely look back kind of wistfully. 9`_9
But I remember last year, when I was playing Crystal, and I'd just gone down to the route below Blackthorn to train my new E-Speed Dratini...
And sent it out into battle.
I was all: "Cool, it's a gir..." O`_O "SHINY SPARKLE?! ... SHINY FEMALE DRATINI WITH EXTREMESPEED! YEEEEEE!"
I proceeded to bounce around the house and talk about how awesome it was to anybody who listened. And who didn't listen (read, everybody). And the next day when I went to school.
Now Amaizumi is a dragonair and never going to evolve (I am SO GLAD it wasn't in a later gen, where she'd be pink rather than a lavendery colour) because shiny dragonite looked silly even then.
...
And a Ruby game from waay, waaaaay back, a donphan, caught as a phanpy in the safari zone.