This query gives you the date of the last FULL backup of each database or gives you the commandline to perform a FULL backup. Adjust this commandline in the query to fit your needs. You could loop through this output to execute the generated comand lines.

select

db.name

, bs.type

, bs.backup_finish_date

, case when bs.type is null

then 'BACKUP DATABASE [' + db.name + '] TO DISK = N''C:\SQL\Backup\' + db.name + '.bak'' WITH NOFORMAT, NOINIT, NAME = N''' + db.name + '-Full Database Backup'', SKIP, NOREWIND, NOUNLOAD, STATS = 10'

else null

end as Backup_command

from

( -- use a sub-select to determine the date of the last FULL backup for each database

select database_name

, type

, MAX(backup_finish_date) as backup_finish_date

from msdb..backupset

where type = 'D'

group by

database_name

, type) bs

right outer join master.sys.databases db

on bs.database_name = db.name

where db.name <> 'tempdb' -- it's not possible to backup the TEMPDB

order by bs.backup_finish_date desc