The procedure to do this is pretty simple and straight forward,
1. Open SQL Server Management Studio
2. Delete or rename mru.dat or SqlStudio.bin file

To help you locate these files, check the below list.

Are you using Windows Server 2003 or Windows XP with SQL Server Management Studio 2005 ?
mru.dat is present at C:\Documents and Settings\username\Application Data\Microsoft\Microsoft SQL Server\90\Tools\Shell

Are you using Windows Server 2008, Windows Vista and Windows 7 with SQL Server Management Studio 2005 ?
mru.dat is present at C:\Users\\AppData\Roaming\Microsoft\Microsoft SQL Server\90\Tools\Shell

Are you using Windows Server 2008, Windows Vista and Windows 7 with SQL Server Management Studio 2008 ?
SqlStudio.bin is present at C:\Users\\AppData\Roaming\Microsoft\Microsoft SQL Server\100\Tools\Shell

Find the file, delete/rename it and now when you open your Sql Server Managment studio all the saved recent connections, username and password will be cleared.

Hope this helps you :)