The big red X on the Work Offline icon confuses many users into thinking the X means they are already offline. While this is true for the large taskbar icon, the Work Offline button on the ribbon always has a red X.
When Outlook 2010 or 2013 is online, the Work offline button looks like a normal button. In addition, depending on your account type, the status bar may say you are online:
When you are working offline, the button is highlighted in yellow (2010) or blue (2013). The status bar should also show that Outlook is offline:
In older versions of Outlook the Work offline command is on the File menu. The status bar icon looks like this:
Some users report that they have problems turning off Work Offline, that Work Offline stays enabled (highlighted or checked) after they click Work Offline to toggle it On. If you are having problems setting Outlook online and are using the Windows Taskbar setting of "Hide", try setting it to always show. Some users report that this simple change allows the setting change to work.