Alright, let's get cracking.
I'm in agreement with Horn. Ash's Froakie/Frogadier/Greninja definitely takes after Ash the most. This will be made evident later in the XYZ series. I'm not going to go and spoil anything. There are plenty of other Pokemon that take after Ash's personality, like Infernape, as stated above, and many others I can't think of at this time.
For Misty, I can't really think of any that truly take after her. I'd say Togetic, but that doesn't really work, since her personality mellows over time from how she used to be. None of her Pokemon really take after her personality, it's kind of hard for me to pinpoint.
For Brock, his Ludicolo takes after him a lot, since, like Brock, Ludicolo fell in love (as a Lombre!), and loves to dance. I always saw a lot of Brock in Ludicolo for some reason, and now that I think about it, this works perfectly for me.
I'm not sure for May, either, all her Pokemon are vastly different from her, but I'd definitely have to say her Blaziken takes the most after May, seeing as it was her first Pokemon she had ever obtained.
As for Dawn, totally agreeing with Buneary. She's very feminine, just like Dawn, and she, also, much like Dawn, didn't change much throughout the entire journey with Ash and Brock. The two of them together, also really like looking nice, so it fits, in various ways.
The Pokemon that takes the most after Iris? ...Dragonite. You'd have to really see where I'm coming from to understand why I picked this. Both are kind of stubborn, in various ways, and Axew was too much of a young one to really take after his trainer.
None of Cilan's Pokemon particularly take after him, except for Pansage. I don't have much to say about this.
For Clemont, his Chespin takes a lot after him, but I really can't think of a though out reason at this time.
Finally, like people have said above me, Serena's Braixen takes the most after her, their interests are similar to one another, and since it was her first Pokemon, they both work well together! Serena's Sylveon, as an Eevee, took after her a lot, too, so both these Pokemon take after Serena's personality, in fact.
