Gen I: Wartortle
It's so cool but cute at the same time. Those fuzzy ears, that tough look in its eyes, that blush, those little fangs, that fluffy tail... *Squee*
Honorable mentions: Lickitung and Mew
Gen II: Shiny Dunsparce
My favorite Pokemon of all. I originally got attached to Dunsparce when trying in vain to evolve it into Gligar as a kid, but what made it my favorite was when I found a Shiny one on Christmas (via PokeRadar) -- the first Shiny I ever found intentionally. I wasn't even using Repels!
Honorable mentions: Ho-Oh, Sneasel, Misdreavus, Furret, Girafarig, and Yanma
Gen III: Nuzleaf and Chimecho
Nuzleaf just looks like a cool, proud little dude (though the females disturb me a little). Chimecho has a cute, unique design.
Honorable mentions: Shedinja and Jirachi
Gen IV: Shiny Mothim and Froslass
Mothim is, in my opinion, the most visually-appealing Shiny of all. Froslass looks elegant, is really quick, and hits hard! Froslass made me fall in love with Ice-types (my default team was an Ice-monotype for a several years). I also like its PBR animation.
Honorable mentions: Leafeon and Shiny Glaceon
Gen V: Vanillite
My favorite food as a Pokemon! Plus, it's adorable (its evolutions, not so much). I just wish they would give it the Snow Warning Ability. :(
Honorable mentions: Purrloin, Oshawott, and Dewott
Gen VI: Meowstic (Male) and Avalugg
I love cats and Meowstic-M is adorable (particularly in its stock Sugimori and Dream World art). Avalugg, while not much of a looker, is really interesting and has awesome Defense (though it dies if hit by a Special Attack). It was also my first MM'd Shiny in XY (hatched as Bergmite).
Mega Evo: Slowbro and Shiny Beedrill
Mega Slowbro looks so derpy -- I love it! Shiny Mega Beedrill just looks really sleek and cool, plus it reminds me of a photo I once took of a green bee.