Normally Microsoft Visio opens all documents in the same instance / window. As with MS Excel, one way around this is to stop opening files by double clicking on them. Instead, you open a new blank Visio window from the start menu, and then open your documents via File > Open.

This works, but is not an ideal solution as it adds a few extra steps every time you want to open more than one document.

Much better would be to open every document in a new Visio instance regardless of how it was opened. Here is a little trick that allows to do exactly that:

• Open Microsoft Visio from the start menu.
• Go to File > Options > Advanced. Scroll down to the General section and enable an option called “Put all settings in Windows registry“. Save changes and close Visio.
  
• Open Windows registry editor (regedit.exe), navigate to HKEY_CURRENT_USER\Software\Microsoft\Office\14.0\Visio\Application and modify a String type entry called SingleInstanceFileOpen. All you need to do is change the value from 1 to 0.
  
• Close the registry editor and try to open couple of Microsoft Vision documents by double clicking on them. They should now open in individual windows.

Windows 7
Microsoft Visio 2010