It’s been well documented now that Microsoft has decided to exclude “Sign as Different User” option from SharePoint 2013. While this was great feature to test SharePoint 2010 capabilities & permissions for different users, it was unnecessary in most cases for production environment.
There has been many hacks and updating out of box files from the SharePoint Root (14 or 15 hive), I personally like the option suggested by Microsoft in one of their KB article – KB2752600
If you are like me and use this feature while testing SharePoint capabilities for multiple users, just type in your browser https://siteurl/_layouts/closeConnection.aspx?loginasanotheruser=true and it should prompt you to enter new user id and password to login as different user.