The script below is a simple and quick way to find out the last backup performed successfully to the databases an SQL server.

select
    s.backup_set_id
    , s.media_set_id
    , s.database_name
    , s.server_name
    , s.name
    , s.recovery_model
    , s.backup_start_date
    ,REVERSE (SUBSTRING (REVERSE (CONVERT (VARCHAR (15), CONVERT (MONEY, DATEDIFF (DAY, s.backup_start_date, GETDATE ())), 1)), 4, 15)) AS days_ago
    ,REVERSE (SUBSTRING (REVERSE (CONVERT (VARCHAR (15), CONVERT (MONEY, ROUND (s.backup_size/1048576.0, 0)), 1)), 4, 15)) AS backup_size_mb
    , s.type
    ,(CASE
        WHEN s.type = 'D' THEN 'Database'
        WHEN s.type = 'F' THEN 'File Or Filegroup'
        WHEN s.type = 'G' THEN 'Differential File'
        WHEN s.type = 'I' THEN 'Differential Database'
        WHEN s.type = 'L' THEN 'Log'
        WHEN s.type = 'P' THEN 'Partial'
        WHEN s.type = 'Q' THEN 'Differential Partial'
        ELSE 'N/A'
        END) AS backup_type
    , f.physical_device_name
from msdb.dbo.backupset s
JOIN msdb.dbo.backupmediafamily f ON s.media_set_id = f.media_set_id
WHERE s.backup_set_id =
(    SELECT TOP 1 a.backup_set_id
    FROM msdb.dbo.backupset a
    WHERE a.database_name = s.database_name
    ORDER BY a.backup_set_id DESC    )
ORDER BY s.database_name