The following script can be used to backup all databases from a SQL server. The system databases are excluded. If any other database should be excluded, add them to the “NOT IN” section.

For different date formats in the export, check: https://robbamforth.wordpress.com/2010/06/11/sql-date-formats-getdate-examples/

The script is exporting the databases now with the following format: databasename_YYMMDD.bak

DECLARE @name VARCHAR(50) -- database name  
DECLARE @path VARCHAR(256) -- path for backup files  
DECLARE @fileName VARCHAR(256) -- filename for backup  
DECLARE @fileDate VARCHAR(20) -- used for file name
 
-- specify database backup directory
SET @path = 'C:\Backup\'  
 
-- specify filename format
SELECT @fileDate = CONVERT(VARCHAR(8),GETDATE(),112) 
 
DECLARE db_cursor CURSOR READ_ONLY FOR  
SELECT name 
FROM master.sys.databases 
WHERE name NOT IN ('master','model','msdb','tempdb')  -- exclude these databases
AND state = 0 -- database is online
AND is_in_standby = 0 -- database is not read only for log shipping
 
OPEN db_cursor   
FETCH NEXT FROM db_cursor INTO @name   
 
WHILE @@FETCH_STATUS = 0   
BEGIN   
   SET @fileName = @path + @name + '_' + @fileDate + '.BAK'  
   BACKUP DATABASE @name TO DISK = @fileName  
 
   FETCH NEXT FROM db_cursor INTO @name   
END   
 
CLOSE db_cursor   
DEALLOCATE db_cursor