My top favorite is definitely Mega Evolution. It was something completely new and unexpected, and it gave several formerly useless Pokemon a chance to become useful in a new way. One of my favorite features in the series.
Some others I really like are these:
Battle Maison: An improvement over the Subway, it made it easier than ever before to get BP, though it is a bit easier to "break" since you can use Megas while your opponents cannot.
Battle Chateau: Excellent place for training and level grinding.
Looker Missions: A good post-game story which I appreciated since I wasn't too fond of the main story.
Hordes: Made EV-training easier than ever before.
I can't pick just one thing, so I'll mention a few (a lot work for both XY and ORAS, but whatever):
Horde battles: I am terrible at Super Training, so I'm glad XY also introduced these to make EV training easier/quicker. I've also caught several shiny Pokemon on both XY & ORAS from Hordes, so there's that too. Mega Evolution: Probably my favourite battle change/mechanic/thing since the Physical/Special split in Gen 4. It's encouraged me to use Pokemon I haven't used much before and/or wouldn't put on a main team before, e.g. Mawile on my Y team. Battle Maison: (Very) frustrating at times, but I find it to be a very easy and fast way to earn Battle Points (Y is the first game where I've ever maxed out my BP).
Other things: Destiny Knot IV breeding, Battle Chateau & Lumiose Restaurants, Pokemon Amie
My top picks would be Mega Evolution, the Friend Safari and Pokémon-Amie. Mega Evolution because it at least several Pokémon a chance that otherwise would be severely overshadowed. Friend Safari due to how rewarding it was because HA Pokémon can be encountered there and all wild Pokémon in the Friend Safari are guaranteed to have at least 2 perfect 31 IVs. Pokémon-Amie because it was so fun to play with your Pokémon and it made Yveltal look cute and allowed me to own a Sylveon horde in Y. But the most notable out of these to me was Mega Evolution because it had a severe impact on the competitive scene, giving Mawile and Kangaskhan a spot in Ubers.
Mega Evolution was my favourite because it made Pokemon that were boring cool again. Also, I loved the exp share because now I didn't have to switch pokemon in and out. However, it made elite 4 a bit too easy.
Man, the looker episode really added something and kept me playing. It was nice and mysterious. I hope Sun/Moon will have something like that too!
I liked the mini games in pokémon amie, for when I had nothing to do.
I liked the character customization alot.
The mega evolution was really fun. The animations looked very cool and to search for the stones was nice too. I had to get used to it though.
I also liked that you had so many friends/rivals, but they should have appeared more often through the storyline.
I liked the rollerskates, and the overall graphics of the game.
Trainer customization, trainer customization, trainer customization!!!
And Battle Chateau so I could quickly raise lots of cash for clothes!
And Lumiose Restaurants/Hotel Risschime so I could play house with that girl character of mine! She'd eat at the restaurants and work at the hotel!
And of course there's the money being made from those places so she could continue expanding her wardrobe!
I'd have to go with Mega Evolution. It was great to see some old favourites get new designs and new typings. I also enjoyed hunting around Kalos for the Mega Stones (although the game exclusive versions were kind of annoying)
I did enjoy the Battle Chateau too. I always enjoy features that enable a rematch with the Gym Leaders. And of course, I am a huge sucker for trainer customisation. I loved being able to change clothes and hairstyle at my leisure,=.
IMO, mega evolution is a nice concept, but they could've implemented it better. Some pokemon were better off with a normal evolution, some pokemon were already OP even before getting a mega and some of the megas are just broken and have underwhelming designs. I still like M.E and want S&M to have them though, bc i love some of the designs and the concept of your pokemon transforming in the middle of the battle just like a Magic girl haha