My overall favorite changes from time to time, and I hate it. -.- But right now, it's Glameow. I like its slight resemblance to the Russian Blue, which is my favorite cat breed; it has a somewhat bluish-gray coat and what-looks-like-an-RB-smile to me. Of all the cat Pokemon, Glameow is the one that I adored the longest (not that I admired all feline Pokes, though). It's simply adorable as well as cute. <3
As for each type that I have a favorite of, well, here's my list:
Normal: As stated above, it's Glameow. Reason's there as well. Next to it is Eevee because I find it adorable.
Fire: Hmm... I'd say Flareon. It's an Eeveelution, it's fluffy, and I just like it.
Ice: Glaceon. Yes, another Eeveelution, but what can I say? I'm a fan. :3 This Ice-type is beautiful.
Grass: Leafeon. It's really the sole Grass-type that I took notice of before Lilligant came along. Oh wait, I also like Roserade. Hooray for flowers! :3
Water: Nope, not Vaporeon; rather, it's... well, I actually don't know, but I like Dewott/Samurott better 'cause among the evolution of the Water-type starters, they're the ones that appealed to me. They're cool~
Electric: I dunno if it's Jolteon or Luxray/Luxio. Jolteon because it's cool and the more dog-like among its family. Luxray/Luxio for the reason that I'm simply fond of them.
Dark: This isn't going to be surprising; it's Umbreon. It's kinda sinister but in a cool way. I think black became my favorite color because of this guy. xD
Ghost: I think it's Chandelure: it's part Fire! :3
Psychic: Espeon~ Another kitty and Eeveelution; it's also pretty.
Dragon: Reshiram. I never really bothered with the Legends or Dragon-types, but this one caught my interest because it's part Fire and I like its design. :3
Bug: Butterfree or Beautifly. I like butterflies. :)
Fighting: Riolu/Lucario or Mienshao. The former duo due to them being cute and cool, respectively, and they're like dogs. The latter... well, it reminds me of Meiling from Cardcaptor Sakura for a reason that I do not know. :o
Flying: Staraptor. It looks awesome and like it owns the other birds... except Braviary, which I also like because it's cool. :D