Golbat in Victory Road, Pokemond Diamond 5 years ago. Still my one and only random encounter shiny, although I have about 10 Pokeradar ones. But Golbat will always be special :) one of my favorite moments in gaming.
Mine was a blue Psyduck in Sapphire's Safari Zone. I was actually able to catch it, surprisingly. --- If you actively hate Justin Bieber... then you don't know what "intended audience" means. Hate Twilight instead, it's far worse.
Electrike in Emerald - I didn't really realise the relevance of it and eventually restarted..
Dugtrio in Platinum - didn't have anything weak enough on me to not one-hit it - was still pretty noobish back then (I always carry a catcher with me now post-game).
First one I actually caught was a Raticate whilst EV training in SoulSilver - almost didn't notice as it's a similar colour and was doing whilst watching TV :P --- http://lparchive.org/Pokemon-Blue/Update%2011/39-capture_13052010_205404.png