Selecting most recent date between two columns

I think the accepted answer is the simplest. However, I would watch for null values in the dates...

SELECT ID,
       CASE WHEN ISNULL(Date1,'01-01-1753') > ISNULL(Date2,'01-01-1753') THEN Date1
            ELSE Date2
       END AS MostRecentDate
FROM Table

CASE is IMHO your best option:

SELECT ID,
       CASE WHEN Date1 > Date2 THEN Date1
            ELSE Date2
       END AS MostRecentDate
FROM Table

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If one of the columns is nullable just need to enclose in COALESCE:

.. COALESCE(Date1, '1/1/1973') > COALESCE(Date2, '1/1/1973')

From SQL Server 2012 it's possible to use the shortcut IIF to CASE expression though the latter is SQL Standard:

SELECT ID,
       IIF(DateColA > DateColB, DateColA, DateColB) AS MostRecentDate
  FROM theTable