When was the last successful backup in sqlserver?

Just right click on the Database and click on properties on the sql management studio.

On top of window the last full backup completion time and log backup completion time is shown.This is the simplest way of finding the success of a daily backup without even typing a command.

Take backup all database from sql server using cursors

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

SET @path = 'C:\Backup\' 

SELECT @fileDate = CONVERT(VARCHAR(20),GETDATE(),112)

DECLARE db_cursor CURSOR FOR 

SELECT name

FROM MASTER.dbo.sysdatabases

WHERE name NOT IN ('master','model','msdb','tempdb') 

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