Error: The msdb database is full (4223074)

Did you have auto growth for db set?

1. From Microsft SQL Server Management Studio, right click on the database and select Properties
2. On the left hand pane, click on Files
3. Click on the AutoGrowth option button
4. Check the "Enable Autogrowth" check box and set the File Growth size to a desired value
5. Under "Maximum File Size", you might want to select the "Unrestricted File Growth" option
   
   

   The msdb database is used by SQL Server Agent for scheduling alerts and jobs and by other features such as Service Broker and Database Mail. By default, the auto growth is enabled for its data and log files. Since msdb database contains the history tables that store backup and restore activities, SQL Server Agent jobs, and database maintenance plans. If you never cleanup the history tables, it may make the msdb database full. To cleanup the history in the msdb database, you could use history cleanup task or execute the sp_purge_jobhistory and sp_delete_backuphistory.

   Reference:
   sp_delete_backuphistory
   http://technet.microsoft.com/en-us/library/ms188328.aspx
   sp_purge_jobhistory (Transact-SQL)
   http://technet.microsoft.com/en-us/library/ms175044.aspx
   History Cleanup Task (Maintenance Plan)
   http://technet.microsoft.com/en-us/library/ms186524.aspx