Microsoft has confirmed that the Xbox One console will require a daily internet connection if you want to keep playing your games library; the DRM requirements are that you will not be able to play the Xbox One after 24 hours of non internet connectivity. You are not forced into having to turn the console on every day, as if you are not home, or just want to leave the system turned off for a few days, then it will need an internet connection as verification before you can play any games.
Quoted by Xbox Wire:
With Xbox One you can game offline for up to 24 hours on your primary console, or one hour if you are logged on to a separate console accessing your library. Offline gaming is not possible after these prescribed times until you re-establish a connection, but you can still watch live TV and enjoy Blu-ray and DVD movies.
Better yet, whilst it has been claimed the Xbox One will play used games or that you can resell your discs Xbox Wire quotes:
Xbox One is designed so game publishers can enable you to give your disc-based games to your friends. There are no fees charged as part of these transfers. There are two requirements: you can only give them to people who have been on your friends list for at least 30 days and each game can only be given once.
Microsoft Studios will enable you to give your games to friends or trade in your Xbox One games at participating retailers. Loaning or renting games won’t be available at launch, but Microsoft are exploring the possibilities in the future.
Via Xbox Wire