Execute the following Microsoft SQL Server T-SQL script in SSMS Query Editor:

SELECT   DISTINCT Name = d.name,

         LastBackup,

         BackupBy = c.user_name

FROM     MASTER.dbo.sysdatabases d

         LEFT JOIN (SELECT   database_name,

                             LastBackup = max(backup_finish_date)

                    FROM     msdb.dbo.backupset

                    WHERE    backup_finish_date <= getdate()

                    GROUP BY database_name) b

           ON d.name = b.database_name

         JOIN msdb.dbo.backupset c

           ON LastBackup = backup_finish_date

ORDER BY name

/*

Name                    LastBackup              BackupBy

AdventureWorks          2010-01-25 04:06:22.000 SRVR\Kevin Miller

AdventureWorks2008      2010-02-07 03:07:10.000 SRVR\Kevin Miller

AdventureWorksDW        2010-08-23 06:59:08.000 SRVR\Kevin Miller

…

*/

Related articles:

Backup Overview (SQL Server)

How Long has it been since that Database was Backed up?