How to detect if a string contains special characters?

Assuming SQL Server:

e.g. if you class special characters as anything NOT alphanumeric:

DECLARE @MyString VARCHAR(100)
SET @MyString = 'adgkjb$'

IF (@MyString LIKE '%[^a-zA-Z0-9]%')
    PRINT 'Contains "special" characters'
ELSE
    PRINT 'Does not contain "special" characters'

Just add to other characters you don't class as special, inside the square brackets

SELECT * FROM tableName WHERE columnName LIKE "%#%" OR columnName LIKE "%$%" OR (etc.)