Does SQL Server Offer Anything Like MySQL's ON DUPLICATE KEY UPDATE

There's no DUPLICATE KEY UPDATE equivalent, but MERGE and WHEN MATCHED might work for you

Inserting, Updating, and Deleting Data by Using MERGE

I was surprised that none of the answers on this page contained an example of an actual query, so here you go:

A more complex example of inserting data and then handling duplicate

MERGE
INTO MyBigDB.dbo.METER_DATA WITH (HOLDLOCK) AS target
USING (SELECT
    77748 AS rtu_id
   ,'12B096876' AS meter_id
   ,56112 AS meter_reading
   ,'20150602 00:20:11' AS local_time) AS source
(rtu_id, meter_id, meter_reading, time_local)
ON (target.rtu_id = source.rtu_id
  AND target.time_local = source.time_local)
WHEN MATCHED
  THEN UPDATE
      SET meter_id = '12B096876'
         ,meter_reading = 56112
WHEN NOT MATCHED
  THEN INSERT (rtu_id, meter_id, meter_reading, time_local)
      VALUES (77748, '12B096876', 56112, '20150602 00:20:11');

SQL Server 2008 has this feature, as part of TSQL.
See documentation on MERGE statement here - http://msdn.microsoft.com/en-us/library/bb510625.aspx