This article saved me quite some headache – also this is the cleanest solution of all. For several other workarounds, see Stackoverflow here.
The solution that works was:
mysqldump -h (your ip) -u (your username) -p --opt --quote-names --skip-set-charset --default-character-set=latin1 (your db name) > (your db name)-dump.sql
mysql -h (your ip) -u (your username) -p --default-character-set=utf8 (your db name) < (your db name)-dump.sql
delete the brackets, dont fill in the brackets (your ip) = 127.0.0.1 for instance