I'm surprised I've never replied to this, but anyway...
Normal - - This has made me realise how bad the normal type pokémon really are on average. I could've picked many normal/flying pokémon over Meowth, but I don't count them.
Fire - - No question, my favourite pokémon of all. There are a lot of great fire types I like, but unfortunately none stand a chance with Typhlosion among them.
Fighting - - Despite there not being as many Fighting Pokémon as some other types, there are a lot of cool choices such as the Machop and Timburr evo lines. Primeape is among my top 5 pokémon overall though so it has no real competition among its type.
Water - - This was a tough choice as there are no stand outs among the type imo, but I think Mudkip is probably my favourite. I like its design and it served me well in the R/S/E era.
Flying - - Similar to Primeape and Typhlosion, Pidgeot is my one of my overall favourites so no real question here. All of the early birds are cool except Unfezant though.
Grass - - It's tough not to pick Ivysaur which I like pretty much equally to Bulbasaur, but I'll hand it to Bulbasaur due to its role in the animé setting it apart. A lot of other cool choices such as Meganium or Victreebel could've been picked, but I just love the Bulbasaur line that bit extra.
Poison - - I was almost tempted to hand this to Victreebel due to the lack of choice among pokémon who have Poison as their primary type, but I remembered the major role Toxicroak played for me on Platinum and decided otherwise.
Electric - - It's tough to exclude Zapdos and Jolteon, but Raichu is my second favourite overall and therefore takes it. While I have used all three for similar amounts of time in the games, I slightly prefer Raichu's design over that of the other two. Pikachu is nothing in comparison to its evolution.
Ground - - There's not a greal deal of choice among this type imo, but I'm happy to pick Groudon as my first game was Ruby. Hopefully we'll see some remakes so I can have him in my team again soon.
Psychic - - There are a lot of cool choices, but for someone who had the first film on video as one of his first Pokémon experiences, there's no other choice than Mewtwo. He's just too badass and I love his backstory, something which few pokémon receive.
Rock - - This really is a poor type to pick from. I've never even used Tyranitar in a game if it helps to put into context how bad the choice really was. I like Tyranitar, but not great amounts.
Ice - - Once again not much choice, but I'm happier picking Articuno than I was picking Tyranitar.
Bug - - Though there is a lot more Bug types than Rock or Ice, I still don't really like many of them. Butterfree is probably within my top ten favourite pokémon which makes it a really easy choice among this type.
Dragon - - There was a lot of choice here, the only Dragon type I don't like is Vibrava (which only has it as a secondary type so I wouldn't have picked it for this type anyway). Dragonite is the original dragon though, it's the best design and it's just the overall coolest. The fact it still remains decent competitively five generations later is cool as well.
Ghost - - This was pretty much between Gengar and Giratina as there aren't many cool Ghosts. Giratina's altered forme doesn't look very good though, so I give it to Gengar.
Dark - - I pick Zoroark mainly due to the role it played for me on Black 2, but its design is pretty cool as well. I could have picked Darkrai or Weavile, but I haven't had the chance to use them as often.
Steel - - This is like a mix of my last two choices, it was only between Cobalion and Dialga and I picked Cobalion due to what it did for me on Black 2. I also narrowly prefer its design to Dialga's.
Fairy - - Obviously this will change as more Fairy species are announced, but Gardevoir is by far the coolest among those announced so far.