You could have a problem with Rudy's code as it doesn't take into account that the last month could be in the previous year. In January month(getdate())-1 would evaluate to 0 which'd match no records.
I've modified Rudy's code a bit and I think it should work.
DECLARE @Now DATETIME
DECLARE @Year INT
DECLARE @Month INT
-- Get month and year of last month
SET @Now = CURRENT_TIMESTAMP
SET @Year = YEAR(DATEADD(month, -1, @Now))
SET @Month = MONTH(DATEADD(month, -1, @Now))
SELECT TOP 10 [FileName],
[DownLoadCount] = COUNT(*)
WHERE MONTH(DateDownloaded) = @Month
AND YEAR(DateDownloaded) = @Year
GROUP BY [FileName]
ORDER BY [DownLoadCount] DESC