Referring to a Column Alias in a WHERE Clause

If you want to use the alias in your WHERE clause, you need to wrap it in a sub select, or CTE:

WITH LogDateDiff AS
(
   SELECT logcount, logUserID, maxlogtm
      , DATEDIFF(day, maxlogtm, GETDATE()) AS daysdiff
   FROM statslogsummary
)
SELECT logCount, logUserId, maxlogtm, daysdiff
FROM LogDateDiff
WHERE daysdiff > 120

SELECT
   logcount, logUserID, maxlogtm,
   DATEDIFF(day, maxlogtm, GETDATE()) AS daysdiff
FROM statslogsummary
WHERE ( DATEDIFF(day, maxlogtm, GETDATE() > 120)

Normally you can't refer to field aliases in the WHERE clause. (Think of it as the entire SELECT including aliases, is applied after the WHERE clause.)

But, as mentioned in other answers, you can force SQL to treat SELECT to be handled before the WHERE clause. This is usually done with parenthesis to force logical order of operation or with a Common Table Expression (CTE):

Parenthesis/Subselect:

SELECT
   *
FROM
(
   SELECT
      logcount, logUserID, maxlogtm,
      DATEDIFF(day, maxlogtm, GETDATE()) AS daysdiff
   FROM statslogsummary   
) as innerTable
WHERE daysdiff > 120

Or see Adam's answer for a CTE version of the same.