According to Microsoft’s Phil Spencer statement, Xbox One will not be able to run any old XBLA games. He also suggested that if you want to keep playing XBLA games, you will have to keep your old Xbox 360.
“Those games will continue to run on your Xbox 360 for as long as your Xbox 360 runs,” he explained. “The box is not backward compatible and we think for somebody who invests in a large digital library that you want to keep your [Xbox 360]. Keep that as a vibrant part of the ecosystem.” he added.
A few days ago, Microsoft said that “if you’re backwards compatible, you’re really backwards”. They have also stated that they will not forget about the Xbox 360 once the new console is out. Considering this, keeping your Xbox 360, as recommended by them, is not such a bad idea.