Yet another option is to cast the XML as nvarchar, and then search for the given string as if the XML vas a nvarchar field.
SELECT *
FROM Table
WHERE CAST(Column as nvarchar(max)) LIKE '%TEST%'
I love this solution as it is clean, easy to remember, hard to mess up, and can be used as a part of a where clause.
This might not be the best performing solution, so think twice before deplying it to production. It is however very usefull for a quick debug session, which is where I mostly use it.
EDIT: As Cliff mentions it, you could use:
…nvarchar if there’s characters that don’t convert to varchar