Games: X and Y
Story wise, X and Y are kinda lackluster. I don't really remember any of the Gym Leaders, they potentially have the worst Elite Four, and their Champion was kinda bleh. The evil team, Team Flame, wasn't too bad, but I still prefer Plasma and the Rockets better. The idea that they were using a legendary Pokemon to fuel power to a destructive weapon was kinda cool, and Lysandre (the leader) was a decent villain.
So why is this entry so high on the list?
This point may seem like cheating and may have even turned a few people off from this game, but I had a huge nostalgia rush as I was playing. In addition to the Greninja I got at the beginning of the game, the professor also allowed me to pick a Generation I starter. Naturally, I enthusiastically welcomed Charizard back to my team and I felt the same as I did all those years ago.
What I liked best about this generation, and the reason I'm still playing it (also, because Gen VII hasn't been officially announced yet) is because of how easy they've now made it to build a team and acquire perfect Pokemon. I've built several teams so far, and I'm planning to go into the next games with a ton of usable Pokemon ready to rock.
On a smaller note, we got (very limited) character customization! Some day my trainer will be able to be bald and bearded! You just wait!
Favorite Pokemon from this Generation:
Greninja, Aegislash, Tyrantrum, Heliolisk, Noivern, and Talonflame.
Team I used my first playthrough:
Greninja, Charizard (Mega), Gardevoir, Heliolisk, Tyrantrum and Aegislash