How do I get the month and day with leading 0's in SQL? (e.g. 9 => 09)

Pad it with 00 and take the right 2:

DECLARE @day CHAR(2)

SET @day = RIGHT('00' + CONVERT(NVARCHAR(2), DATEPART(DAY, GETDATE())), 2)

print @day

For SQL Server 2012 and up , with leading zeroes:

 SELECT FORMAT(GETDATE(),'MM') 

without:

SELECT    MONTH(GETDATE())

Use SQL Server's date styles to pre-format your date values.

SELECT
    CONVERT(varchar(2), GETDATE(), 101) AS monthLeadingZero  -- Date Style 101 = mm/dd/yyyy
    ,CONVERT(varchar(2), GETDATE(), 103) AS dayLeadingZero   -- Date Style 103 = dd/mm/yyyy