EDIT: This stored procedure has been updated.

This stored procedure performs a full backup of the databases.  It has two input parameters.  The first input parameter 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.  The second input parameter is to control which databases you want to backup.  You can pass it All, System, or User.  All means backup all databases (except tempdb of course).  System means backup master, model, and msdb.  User means backup the user databases. 

I have heavily commented it so that it is easier to understand.  I am not normally so verbose in my coding.

I've also got a SQL Litespeed stored procedure that is very similar to this one.  I'll post that one soon.

----------------------------------------------------------------------------------------------------
-- OBJECT NAME         : isp_Backup
--
-- AUTHOR               : Tara Duggan
--
-- INPUTS    : @Path - location of the backups
--        @dbType - which databases to backup - All, System, or User
-- OUTPUTS    : None
-- DEPENDENCIES         : None
--
-- DESCRIPTION         : This stored procedure performs a full backup on all of the user databases
--
-- EXAMPLES (optional)  : EXEC isp_Backup @Path = 'F:\MSSQL\Backup\', @dbType = 'All'
----------------------------------------------------------------------------------------------------
CREATE          PROC isp_Backup
(@Path VARCHAR(100), @dbType VARCHAR(6))
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 @filename VARCHAR(200) -- stores the path and file name of the BAK file

CREATE TABLE #WhichDatabase
(
 dbName SYSNAME NOT NULL
)

-- Get the list of the databases to be backed up
IF @dbType = 'All'

 INSERT INTO #WhichDatabase (dbName)
 SELECT [name]
 FROM master.dbo.sysdatabases
 WHERE [name] <> 'tempdb'
 ORDER BY [name]

ELSE
BEGIN

 IF @dbType = 'System'

  INSERT INTO #WhichDatabase (dbName)
  SELECT [name]
  FROM master.dbo.sysdatabases
  WHERE [name] IN ('master', 'model', 'msdb')
  ORDER BY [name]

 ELSE
 BEGIN

  IF @dbType = 'User'

   INSERT INTO #WhichDatabase (dbName)
   SELECT [name]
   FROM master.dbo.sysdatabases
   WHERE [name] NOT IN ('master', 'model', 'msdb', 'tempdb')
   ORDER BY [name]

  ELSE
  BEGIN

   DROP TABLE #WhichDatabase

   RETURN -1

  END

 END

END

-- 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 @filename = @Path + @DBName + '\' + @DBName + '_' + @Now + '.BAK'
 
 -- 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 '%