Ah, neat, a brain excercise. I'm so used to just exclaiming Nidorina and being done with it (mostly because I can't remember anyone else 80% of the time) that this'll give me a chance to actually think back and evaluate.
Normal: Er, well I'm already off to a bad start. I can't choose between Sentret, Rattata and Miltank, but the reasons are all the same. I just think all of them are cute. Rattata gets bonus points just for being a rodent, the type of animals I like iRL.
Fire: Vulpix. Has been my favorite for over a decade based on the sheer novelty of being adorable, and having a voice to match. I know most people prefer Eevee, but I feel Vulpix outclasses Eevee at least ten-fold.
Water: Oh, shoot. I dunno. Totod... Mudk, well, no, Squirt... AHA. Lapras. No. No, wait. Totodile. Definately, definately Totodile. Probably. As for why, well, it's one of those "depends on the artist" sort of things, but Totodile can be really cute, too. I bought a Totodile plushie from the Pokemon Store in NY way way way back, and it's the cutest chibification of it ever. Lapras is graceful, but I think Totodile edges it out just for its playful personality. And cute appeal if that's what the artist is aiming for.
Oh shoot. I totally forgot Horsea. Horsea's probably a runner up. I just wish it wasn't edged out by Togepi in the anime.
Electric: Flaaffy, no contest. Also cute as a button. Clearly, I'm aesthetically biased.
Grass: It's between the first three generations of starters. Chikorita is on the far end of cute, Treecko's on the far end of cool, and Bulbasaur sits in the middle. My actual preference flucuates, typically between Chiko and Bulba, with Treecko poping in on the days I remember the poor guy actually exists. There's no way I can settle on one.
Ice: Articuno, I guess. I can't remember a whole lot of ice types. But I always loved this thing's cry in the games. That's one thing I'll probably never forget.
Ground: Is Trapinch a ground type? If so, him. Those starry eyes and that huge head of his on that little body, man I love it.
Fighting: Hitmontop or Medicham (depending on the artist). Hitmontop is sort of funny looking, but not goofy funny. Like Charlie Brown funny. It's a very simple design that I can get behind. Medicham, it really does come down to who's drawing it, because it has potential, but it can also come off as too weird.
Poison: Nidorina. The easiest one thus far. There's way way way way way too many reasons why I like Nidorina, that I can't possibly condense it into something bite-sized. You'll just have to trust me when I say Nidorina's my favorite Pokemon (but for the sake of the topic, I'll throw out good character design as one of the core reasons).
Flying: Aye... Pidgey? It's a successful take on the common sparrow, I'll give it that. The name just doesn't match at all.
Psychic: Kirlia for historical reasons, but otherwise I'm not sure. Mew may be a modern answer for me, though, sense I don't pay Kirlia any attention anymore. Also, sometimes it's Abra. Blah, this list really isn't working for me, is it?
Dark: Sableye, if it's really dark-ghost and I'm not just remembering wrong. Funny looking creature that reminds me of Stitch from Lilo and Stitch.
Bug: Parasect. If I don't like a Pokemon because it's cute, I love it because it's goofy. What a funny looking creature this guy is. I love how it has a face like 83. Paras is cuter, but Parasect makes me laugh, and that's good enough.
Rock: Onix. I have to give Brock's Onix credit more making me think of it as more than a huge, mean ol' rock snake. It seems like there's some compassion underneath that rocky exterior. I'd like to think that Onix are contemplative to a degree. Imagining stuff like this is why I still like Pokemon.
Ghost: Haunter. Much better looking than Gengar, and the character design is appealling overall.
Dragon: Flygon. One of the few dragons I actually like beyond a superficial level. I mean, the Dratini line is a favorite of mine, too, but I never feel compelled to give them a lot of thought, either.
Steel: Mawile. Almost solely on the basis that there aren't any other cute steel types that I can identify with, Aron being an exception. Whether or not they came up with some in the 4th generation and beyond, I wouldn't know, and I lack the will to find out. I have to go with what I know.
Ugh, terrible. This is the result of someone who hasn't played Pokemon in ages, folks, but still loves them enough as characters.