Twilight: Would be hopefully sorted in Ravenclaw by anyone :D Our lovely responsible egghead~
 
Rainbow Dash: Another easy to sort. Brave, loyal and sort of boastful. Griffindor it is.
 
Applejack: Honest, stable, patient and somehow modest. That’s Hufflepuff. Some say she should be in Griffindor. Well, she could be but even according to the Pottermore site Hufflepuff and Griffindor are very close to each other. Applejack and Rainbow Dash demonstrate the difference pretty well, I think :)
 
Fluttershy: Well, where else should this kind, nice and not-much-assertive pony belong? She fits so perfectly to the description of the Hufflepuff badger - hiding in her den but when her home/family/friends are in danger, she comes out and fights.
 
Gilda & Trixie: None of the Mane-6 seemed to fit in Slitherin and when you think about it, how often do Slitherins get along with the other houses? They are not evil, no - but they may not be always entirelly good. Trixie and Gilda are ideal MLP characters to sort in Slitherin I think :D
 
Rarity: Now, here comes one of the two ponies who were harder to sort. In the end I put Rarity in Ravenclaw because I realized I can’t imagine her being in Griffindor. And Ravenclaw is supposed to support creativity so Rarity might fit well there (plus she’s an unicorn, isn’t she).
 
Pinkie Pie: Pinkie could be probably in any of the houses except Slitherin. Ravenclaw also supports individuality - that would fit well to her (because how would you describe Pinkie in other words than “Pinkie”…?). But she likes all those little jokes and is so enthusiastic… Put the Weasley twins and Colin Creevy together and you might get a similar character, so Pinkie to Griffindor :)
 
As for the heads of the houses, Discord is clear. Hey, I would even like to go to that house because of him XD. I love Discord :D
 
The rest are alicorns - just because alicorns are always one lvl higher than the rest - good for the head teachers. Celestia is clear as well xD Where else should she be? She’s our little winged Dumbledore - she even has a phoenix xD
 
Not that there were any mentions of Luna the egghead or whatever, but she’s blue and flies, so that’s it.
 
As for Cadence (hey, is it Cadence or Cadance? __), that girl just makes a perfect third alicorn to be a head teacher. She’s not strong in terms of power, she’s kind and nice, happy (if no Chrysalis around) and really loyal as well. Hufflepuff :)