Recently I was having some problems with using Add-AzureAccount in PowerShell.
I could sign in correctly but as soon as I tried any Azure cmdlet I would get the error "No default subscription has been designated".
This error kept showing up, also after Remove-AzureAccount, restarting PowerShell or PC.
After searching I found this folder (C:\Users<User Name>\AppData\Roaming\Windows Azure Powershell) where account information is cached by Azure PowerShell.
Deleting the content of that folder, and restarting PowerShell fixed the problem.