EDIT: Now you can start building your Xbox One games library from your Xbox 360. Just go to "Games with Gold" from the Gold tile on Home.
For a while now Microsoft has been giving away free games to their Xbox live gold members twice a month. When the Xbox One came out they included the same deal. You can get Xbox One games for free as a gold member. Originally I thought that you had to own a Xbox One to use this benefit. But one day I discovered that you can "purchase" these free games through their website (http://www.xbox.com/en-US/live/games-with-gold).
This is awesome because I don't own the Xbox One, yet. So Twice a month I visit xbox.com and claim my free games for the Xbox One. This way when I finally have enough saved up enough to buy it, I'll already have plenty of games to enjoy. I just wish I discovered this sooner, because I haven't found a way to go back and claim the free offers I missed.
Note: This also works for those that don't have enough hard drive space for all their games. You can still claim your free game and just wait to download it.
Here are instructions on re-downloading online purchases content. (http://support.xbox.com/en-US/xbox-360/downloadable-content/redownload-content)