I will not repeat entries below. Once a Pokemon is mentioned for a type, it's not being mentioned again, even if it's part something. (For example, Parasect is part Grass, but I won't mention it under the Grass category.)
Also, I put stars ( * ) next to the Pokemon that actually make my all-time favorite Pokemon list.
Bug: Heracross, Venomoth*, and Parasect
Reason: I've always liked Ash's Heracross for one reason or another as well as the general design of the Pokemon. Venomoth and Parasect, meanwhile, have gotten me through some tough bits of the game. (My old Parasect on Red, for example, once downed Mewtwo.)
Dark: Sneasel and Absol
Reason: Design only. Although I once had a pretty good Absol on my first time through Sapphire.
Dragon: Flygon
Reason: Design, mainly, and I'm pretty fond of the ones I've raised.
Electric: Raichu* and Electabuzz*
Reason: I've always been a Raichu fan, ever since I first saw "Electric Shock Showdown." I just can't resist how cute it is. Electabuzz, meanwhile, got me through quite a few ASB and in-game matches.
Fighting: Medicham* and Breloom
Reason: Medicham is one of my all-time favorite Pokemon, what with its awesome moves (move that got me through Sapphire, no less). Breloom, meanwhile, still holds a place in my heart just for being that quirky.
Fire: Arcanine
Reason: Dude, this thing blitzed Steven's Metagross in Ruby. In one hit. And it was a level under 'Gross. That should say enough.
Flying: Crobat
Reason: I love how sleek and speedy Crobat is. It can Haze or Toxic before a lot of other Pokemon. Not all of them, but a lot of them.
Ghost: Haunter*
Reason: I blame this completely on "The Tower of Terror" and "Haunter versus Kadabra." And its design is just awesome.
Grass: Cradily and Celebi
Reason: Mainly because I had fun raising the one I've got in Sapphire. Celebi, meanwhile, is my favorite legendary, simply because I think it's adorable (despite the fact that Megahorn can blitz it).
Ground: Marowak and Quagsire
Reason: Because the Marowak I've raised are awesome. Quagsire makes the list, meanwhile, because it's quirky, and I like that.
Ice: Jynx
Reason: More for the fact that she got me out of some good ASB matches than the fact that she's so controversial.
Normal: Rattata* and Kecleon*
Reason: Rattata because it's cute and packs a punch with its fangs, and Kecleon because it's annoying yet useful with Color Change. And it's cute, in my opinion.
Poison: Arbok
Reason: Because Jessie's rocked.
Psychic: Gardevoir*
Reason: Favorite Pokemon OF ALL TIME. It's elegant, powerful, and even loyal according to its 'dex entries. And its sweet little cry makes me squeal fangirlishly when I hear it. (Yes, I'm a freak.) Not to mention its natural traits (Synchronize and Trace -- especially Trace) are simply awesome.
Rock: Golem
Reason: Because it got me through Crystal.
Steel: Scizor
Reason: Because of its design, really. Sleek, yet powerful.
Water: Squirtle*
Reason: I blame this completely on Ash's Squirtle (as well as the ones I've raised myself).