Accessing Digital Game Library on Different 360 Console

Yes you can access them, but you have to download them to the console. Log in with your account, then goto settings - account - download history. Scroll down to the games you want to download, select them and start the download. Once they have finished
you can then play.

You can still play the content on a new console as long as you're signed in to Xbox Live using the gamertag that originally purchased the content. To download games you own

1. Sign in to Xbox Live using the gamertag that you used when you originally purchased the content.
   
2. Go to settings and select Account.
3. Select Download History.
4. Browse your download history. If you want to download something again, select the item, and then select
   Download Again.

@Stud

The majority of this discussion has been about playing a single purchase at the same time rather than sharing access to a library. Proving that a single license was being played by two different people at the same time would be easy to do if they choose
to, especially when most of us are online all the time anyway.

Sharing access to a digital game library isn't much different than loaning a friend your disc so I don't see them being to concerned about it. Two people playing Titanfall at the same time from different consoles just cost them a sale and that's where their
concern is going to be. As more people go digital and figure out sharing a "home console" is more economical it could take a huge chunk out of sales.

dainja

Agreed. And as I have internet access, it's essentially a non-issue, so I'm making my decision based on the other features of the console - such as multitasking, a digital library, seamless switching - and, of course, the games.

Theoretically, any digital copies from the Microsoft library would be accessible on PC if made available. It's more unlikely you would ever be able to pop a 360 disc into a PC to play.