These two querys gives me the exact same result:
select * from topics where name=\'Harligt\'; select * from topics where name=\'Härligt\';
you want to check your collation settings, collation is the property that sets which characters are identical.
these 2 pages should help you
http://dev.mysql.com/doc/refman/5.1/en/charset-general.html
http://dev.mysql.com/doc/refman/5.1/en/charset-mysql.html