Microsoft actively working on a fix
[Update: Microsoft has issued a statement regarding the service troubles.
Microsoft is investigating an issue that may interrupt customer access to some Microsoft online services. This is unrelated to the launch of “Titanfall” and the Xbox Live service is up and running. The issue on Xbox is resolved, but unfortunately a small percentage of Xbox One owners may still experience a sign-in issue on Xbox Live, which can be fixed with a cold reboot of the Xbox One by powering down, unplugging, waiting 10 seconds, plugging back in and powering back on. The Xbox team sincerely apologizes for the interruption.]
Xbox Live is experiencing some troubles at the moment. Users aren't able to sign-in to their accounts, and having some issues connecting to matchmaking. Xbox's Major Nelson has addressed the issue, and Microsoft is actively working on a fix.
The Major notes this isn't a Titanfall issue, but that along with the newly launched Twitch app probably isn't helping the situation. Note that this issue isn't affecting all users either. You can check-in on the status of the service over on the Xbox support page.