*cracks knuckles and assembles list... with explanations where possible*
Some have multiple votes, yeah, but I'll try not to put more than two down as my favorite of any type.
And no, I will not do repeats, mostly because that's not much of a challenge.
Bug: Beedrill and Parasect
Both because of fond memories. Beedrill kicked many a tail back in RBY to the point where I owned one in almost every game, if only to take care of Sabrina. Parasect, meanwhile, I fell in love with in GSC, when I started realizing that Spore + False Swipe was a really cool combination for catching Pokemon... and that Spore + Slash was awesome against the in-game trainers and a few of my friends.
Dark: Poochyena
I blame this one on an RPG I once played, where someone went and gave one of my characters a ridiculously cute Poochyena. I now cannot see one without breaking into "aww" after "aww."
Dragon: Flygon
I've always liked the design, and raising one wasn't so bad either. (Unlike attempting to do things like raise a Dragonite.)
Electric: Raichu
Fond memories. I got one in RBY because of the anime, and it pwned whatever Beedrill didn't pwn. That and I always thought it was absolutely adorable.
Fighting: Breloom
Seriously. Funky mushroom kangaroo kicking the crap out of things? I like it.
Fire: Growlithe and Houndoom
Growlithe is actually the result of a failed fanfiction I wrote but never posted awhile ago. The idea was crap, but I walked away thinking Growlithe was a cute and pretty cool Pokemon in itself and so started to raise them in Red. Houndoom is actually because of another RPG and can be summed up with the phrase, "Hey, you can do some pretty cool things with a Houndoom."
Flying: Crobat
Mostly because of RSE. I raised a Crobat in Sapphire, and she seriously kicked tail.
Ghost: Haunter
Something I fully blame on the anime.
Grass: Cradily
Mostly because of a combination of design, having one in Sapphire and liking it, and inside jokes. (Oh, come on. Like it's not possible to think the same thing with those tentacles.)
Ground: Sandslash
Design, mostly.
Ice: Cloyster
Because I thought Lorelei was the coolest trainer ever at one point. Also, having one that kicked tail helped too.
Normal: Furret
From the same RPG that involved the ridiculously cute Poochyena. That prompted me to raise one, which, in my last game on Silver, was seriously the leader of my team. It was cute, and it put most trainers I came across in their places. I just loved my Furret (which I thankfully had the sense to transfer across to my copy of Crystal before restarting).
Poison: Arbok
Partly design, partly the fact that I have always loved Jessie's.
Psychic: Gardevoir
My absolute favorite Pokemon at the moment, and with good reason. At first, I just loved Ralts, so I caught one in Sapphire and trained it. Kirlia wasn't a thrill, but then, I got a Gardevoir and decided to check my 'dex entry about the species. And hocrap, I was impressed. Just the idea of the dedication a Gardevoir had for its trainer seemed awesome in itself (as was the ability to create black holes), so I kept him on my team, gave it a few new moves (like Calm Mind and Thunderbolt), and proceeded to kick tail with him. And that just won me over. Design, power, dedication -- absolutely adore this Pokemon.
Rock: Aerodactyl
Fond game memories, mostly. And owning people online with it.
Steel: Skarmory
Also fond game memories (although the one that has sparked these memories was, admittedly, a really crappy Skarmory in every way possible). To this day, I just find that there's something about Skarmory that makes it seem tougher and more awesomely ferocious than the other Steel-types to me.
Water: Starmie and Squirtle
Both because of fond game memories. Squirtle was my first starter and is currently my traditional starter whenever I start a new game on RB or FrLg. (That is, unless I'm trying to get another legendary beast in the latter.) This is mostly because Ash's Squirtle had to have been my favorite among his Pokemon at the time, so naturally, I wanted one just as cool. Starmie, meanwhile, is just because I own one in an ASB league on another board, and it's saved my tail now and then.