EDIT: This stored procedure has been updated.

The below stored procedure will backup the transaction log for each of the databases that aren't being log shipped (you don't want to break  log shipping by running a transaction log backup outside of the log shipping plan) and also aren't using SIMPLE for the recovery model.  It has one input parameter, which is the path to where you would like to backup the databases.  It'll create a sub directory underneath that path for each of the databases.  It also deletes any files that are older than two days in that sub directory.  If a sub directory doesn't exist, it creates one for you. 

I've got three more DBA maintenance stored procedures (DBREINDEX, INDEXDEFRAG, and my own version of sp_delete_backuphistory that doesn't use a cursor) that I'm going to post soon.

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-- OBJECT NAME         : isp_Backup_TLog
--
-- AUTHOR               : Tara Duggan
-- INPUTS    : @Path - location of the backups
-- OUTPUTS    : None
-- DEPENDENCIES         : None
--
-- DESCRIPTION         : This stored procedure performs a transaction log backup on the non-log
--        shipped user databases that do not have SIMPLE set as the recovery model.
--
-- EXAMPLES (optional)  : EXEC isp_Backup_TLog @Path = 'F:\MSSQL\Backup\'
--
-- MODIFICATION HISTORY :
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--
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CREATE        PROC isp_Backup_TLog
(@Path VARCHAR(100))
AS

SET NOCOUNT ON

DECLARE @Now CHAR(14) -- current date in the form of yyyymmddhhmmss
DECLARE @DBName SYSNAME -- stores the database name that is currently being processed
DECLARE @cmd SYSNAME -- stores the dynamically created DOS command
DECLARE @Result INT -- stores the result of the dir DOS command
DECLARE @RowCnt INT -- stores @@ROWCOUNT
DECLARE @disk VARCHAR(200) -- stores the path and file name of the TRN file

CREATE TABLE #WhichDatabase
(
 dbName SYSNAME NOT NULL
)

-- Get the list of the databases to be backed up
INSERT INTO #WhichDatabase (dbName)
SELECT [name]
FROM master.dbo.sysdatabases
WHERE  [name] NOT IN ('master', 'model', 'msdb', 'tempdb') AND
  [name] NOT IN (SELECT database_name FROM msdb.dbo.log_shipping_databases) AND
  DATABASEPROPERTYEX([name], 'Recovery') <> 'SIMPLE'
ORDER BY name

-- Get the database to be backed up
SELECT TOP 1 @DBName = dbName
FROM #WhichDatabase

SET @RowCnt = @@ROWCOUNT

-- Iterate throught the temp table until no more databases need to be backed up
WHILE @RowCnt <> 0
BEGIN

 -- Get the current date using style 120, remove all dashes, spaces, and colons
 SELECT @Now = REPLACE(REPLACE(REPLACE(CONVERT(VARCHAR(50), GETDATE(), 120), '-', ''), ' ', ''), ':', '')

 -- Build the .BAK path and file name
 SELECT @disk = @Path + @DBName + '\' + @DBName + '_' + @Now + '.TRN'
  
 -- Build the dir command that will check to see if the directory exists
 SELECT @cmd = 'dir ' + @Path + @DBName

 -- Run the dir command, put output of xp_cmdshell into @result
 EXEC @result = master.dbo.xp_cmdshell @cmd

 -- If the directory does not exist, we must create it
 IF @result <> 0
 BEGIN
  
  -- Build the mkdir command  
  SELECT @cmd = 'mkdir ' + @Path + @DBName

  -- Create the directory
  EXEC master.dbo.xp_cmdshell @cmd, NO_OUTPUT

 END
 -- The directory exists, so let's delete files older than two days
 ELSE
 BEGIN

  -- Stores the name of the file to be deleted
  DECLARE @WhichFile VARCHAR(1000)

  CREATE TABLE #DeleteOldFiles
  (
   DirInfo VARCHAR(7000)
  )

  -- Build the command that will list out all of the files in a directory
  SELECT @cmd = 'dir ' + @Path + @DBName + ' /OD'

  -- Run the dir command and put the results into a temp table
  INSERT INTO #DeleteOldFiles
  EXEC master.dbo.xp_cmdshell @cmd

  -- Delete all rows from the temp table except the ones that correspond to the files to be deleted
  DELETE
  FROM #DeleteOldFiles
  WHERE ISDATE(SUBSTRING(DirInfo, 1, 10)) = 0 OR DirInfo LIKE '%