One of the biggest features that was introduced to us last generation was the Dream World. You could explore it to find hidden items, find Pokémon with alternate abilities, and the only ways to obtain berries without transferring them from previous games. It integrated using Pokémon's website into the games directly for the first time, allowing them to explore certain ares to find certain Pokémon, as well as giving mini-games that would allow the player to encounter a Pokémon depending on how well they played the game.
Sort of similar to this concept was the Pokéwalker, which allowed you to take steps and level up your Pokémon. You could also encouter wild Pokémon to capture depending on which course you were walking on, and then send it back to your game if you so chose to do so.
The question here is, would you like to see the Dream World make a return for X and Y? Are there any specific features you would definitely bring back, or anything you could live without? How about other things that can affect your game that you aren't doing directly in it? Would you like another feature on the Pokémon website to play around with to earn rewards?