Nintendo has acknowledged a game-breaking glitch affecting some Pokemon X and Y players on its Japanese site (via NintendoLife). The glitch can occur when players save in the outer ring of Lumiose City's streets, causing the system to freeze whenever that save is loaded.
The Nintendo page advises players to avoid saving in the region outlined in blue below until the issue can be resolved. It recommends players save in the city's buildings instead--you might as well stick to the tradition and save only in Pokemon Centers.
If you've already encountered the problem, all is not lost: Nintendo plans to release an update or other means of repairing the game over the eShop in the near future. Keep in mind that this information was on the Japanese site, so it may take a bit longer to hit the U.S. and Europe.