source: https://www.mssqltips.com/sqlservertip/1070/simple-script-to-backup-all-sql-server-databases/

Change @Path for the location of the backups.

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(20),GETDATE(),112)
 
— specify filename format Including Time
— SELECT @fileDate = CONVERT(VARCHAR(20),GETDATE(),112) + ‘_’ + REPLACE(CONVERT(VARCHAR(20),GETDATE(),108),’:’,”)
 
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 
 WITH STATS, COMPRESSION, COPY_ONLY
   FETCH NEXT FROM db_cursor INTO @name  
END  
 
 
CLOSE db_cursor  
DEALLOCATE db_cursor