For me it's:

Water: Totodile.
Flying: Pidgeot.
Rock: Rampardos.
Electric: Manectric and Pikachu both.
Dragon: Garchomp.
Grass: Roserade.
Poison: ...
Ground: Sandslash.
Bug: Scyther.
Dark: Sneasel.
Ice: Froslass.
Steel: ...
Fighting: Hitmonlee.
Pshychic: Latias/Espeon.
Normal: Linoone.
Ghost: Shuppet.
Fire: Chimchar.

Man, I can never name just one. (Some dual-type pokemon might even end up in my list more than once. ^_^)
*Also includes evolutions

Grass: Chikorita*, Breloom, Treecko*
Fire: Cyndaquil*, Blaziken, Houndour*, Growlithe*, Vulpix*
Water: Squirtle (thanks to Brawl ^_^), Lapras, Totodile*, Milotic
Electric: Pikachu* (mandatory =P), Luxray
Ice: Lapras, Froslass
Psychic: Hypno, Xatu, Gallade
Dragon: Dragonair, Horsea* (they're dragons in my head, thanks to Kingdra ^_^), Salamence
Dark: Sneasel, Houndour*, Absol
Fighting: Lucario, Gallade
Flying: Pidgey*, Taillow*
Poison: Nidoran* (both genders and all evos),
Ground: Donphan
Rock: Larvitar* (but not Pupitar), Rhydon,
Steel: Lairon* (not Aron <_<),
Bug: Scyther*, Heracross, Yanmega
Ghost: Gastly*, Duskull
Normal: Eevee* (evos are favorites in their respective types), Zangoose

And of course, chances are I forgot a bunch. Left out legendaries on purpose.

Water: Milotic.
Flying: Drifblim
Rock: Cradily!
Electric: Raichu
Dragon: Flygon
Grass: Roserade or Tangela/Tangrowth. Probably Tangrowth though. ^_^
Poison: Erm.. not really fond of Poison-types. But if I had to choose, it'd be Nidorina.
Ground: Gastrodon
Bug: Butterfree!
Dark: Weavile
Ice: Froslass! Although Weavile's in second. lol
Steel: Mawile
Fighting: Lucario or Gallade.
Psychic: Ralts family. That wasn't obvious, now was it? :]
Normal: Clefable hands down. I can't believe I nearly left it out of my UU team!
Ghost: Gastly family.
Fire: Ninetales or Blaziken. ^_^

Water: Starmie
Flying: Swellow
Rock: Cradily
Electric: Magneton
Dragon: Palkia
Grass: Victreebel
Poison: Vileplume
Ground: Marowak
Bug: Vespiquen
Dark: Umbreon
Ice: Regice
Steel: Mawile
Fighting: Lucario
Psychic: Alakazam, Exeggutor
Normal: Regigigas
Ghost: Haunter
Fire: Heatran

Tina wrote:

Rock: Cradily!

Finally, some appreciation!

_________________

Water: Azumarill.
Flying: Altaria.
Rock: Sudowoodo.
Electric: Jolteon.
Dragon: Flygon.
Grass: Roserade.
Poison: Muk.
Ground: Golem.
Bug: Pinsir.
Dark: Umbreon.
Ice: Glaceon.
Steel: Aron.
Fighting: Tyrogue.
Psychic: Espeon.
Normal: Linoone.
Ghost: Haunter.
Fire: Chimchar.

Water: Azuril
Flying: Starly
Rock: Bonsly
Electric: Rotom
Dragon: Flygon
Grass: Bulbasaur
Poison: Muk.
Ground: Geodude
Bug: Scyther
Dark: Umbreon
Ice: Froslass
Steel: Skarmory
Fighting: Machop
Psychic: Espeon
Normal: Skitty, Clefairy and Teddiursa evenly.
Ghost: Haunter
Fire: Chimchar, Ninetails, and Flareon evenly.

Water: Vaporeon
Flying: Swellow
Rock: Rampardos
Electric: Jolteon
Dragon: Dragonar
Grass: Balbasur
Poison: Koffing
Ground: Sandshew
Bug: Scyther
Dark: Umbreon
Ice: Glaceon
Steel: Steelix
Fighting: Hitmonchan
Pshychic: Espeon
Normal: Eevee
Ghost: Shuppet
Fire: Flareon

Well, where to start:

Fire: Torchic
Water: Piplup
Grass: Roserade
Thunder: Jolteon
Flying: Skarmory
Ice: Abomasnow
Psychic: Spoink and Grumpig
Dragon: Bagon and Salamence
Steel: Empoleon
Dark: Umbreon
Poison: Crobat
Fighting: Breloom
Ground:Swampert
Bug:Yanmega
Rock: Bastiodon
Ghost: Drifloon
Normal:Porygon Z

Fire: Flareon
Water: Vaporeon
Grass: Leafeon
Electric: Jolteon
Flying: Dragonite
Ice: Glaceon
Psychic: Espeon
Dragon: Dragonite
Steel: Lucario
Dark: Umbreon
Poison: Roserade
Fighting: Lucario
Ground: Garchomp
Bug: Butterfree
Rock: Rampardos
Ghost: Gengar
Normal: Eevee

You sure do like Eevees alot.

Because Eevees are awesome. =P

That's why I tried to keep Eevees out of my list as much as possible lol. I only left in Espeon because its genuinely one of my favorite psychics, not just because it's an Eeveelution. =P

Water: Starmie
Flying: Jumpluff
Rock: Cradily
Electric: Raichu
Dragon: Gibble
Grass: Breloom
Poison: Tentacruel
Ground: Diglett
Bug: Heracross
Dark: Umbreon
Ice: Mamoswine
Steel: Fortress
Fighting: Lucario
Psychic: Metagross
Normal: Snorlax
Ghost: Gengar
Fire: Infernape

Fire: Flareon
Water: Vaporeon
Grass: Sceptile
Electric: Jolteon
Dragon: Dragonite
Psychic: Gardevoir
Fighting: Gallade
Dark: Absol
Bug: Scyther
Flying: Salamence
Ice: Glaceon
Rock: Tyranitar
Ground: Dugtrio
Steel: Lucario
Normal: Eevee
Poison: Seviper (still wouldn't use it)
Ghost: Dusknoir (still wouldn't use it)

Yes, Eevee are awesome.

Water: Milotic
Flying: Jumpluff
Rock: Onix
Electric: Jolteon
Dragon: Dragonair
Grass: Sceptile
Poison: Muk
Ground: Rhyperior
Bug: Butterfree
Dark: Umbreon
Ice: Lapras
Steel: Steelix
Fighting: Machamp
Psychic: Espeon
Normal: Miltank
Ghost: Gengar
Fire: Charizard