Another option is to use
UNION ALL[
^].
SELECT ColName, AvgValue
FROM (
SELECT 'Avg1' AS ColName, AVG(Col1) As AvgValue
FROM TableName
UNION ALL
SELECT 'Avg2' AS ColName, AVG(Col2) As AvgValue
FROM TableName
UNION ALL
SELECT 'Avg3' AS ColName, AVG(Col3) As AvgValue
FROM TableName
) AS T
Tested example:
SqlFiddle[
^]