We apologize for any inconvenience, but we've made the site read only while we're making some improvements.

When I browsed the site I got the following message: “We apologize for any inconvenience, but we’ve made the site read only while we’re making some improvements.”

Reason: 

The reason was backup of this specific site collection did not complete successfully. When you backup a Site, SharePoint places the site in read-only mode. But since my backup hanged the site never got out the read-only mode.

Solution:

• Go to Central Administration.
• Under Application Management go to "Configure quotas and locks".

• Set Site lock information to "Not locked". 

 But it was grayed out and I couldn't change it directly.

Luckily since the April 2013 CU update for SharePoint 2013 we now have the SpsiteAdministration.ClearMaintenanceMode method. So we can clear the flag with the flowing two lines:

    $site = new-object Microsoft.SharePoint.Administration.SPSiteAdministration(‘http://intranet.demo.local’)
    $site.ClearMaintenanceMode()

and your site is out of maintenance mode again!