If you try to convert your wordpress blog (any version previous to 2.2) you can have problems with the caracters because last versions use UTF-8.
The automatic conversion through Cpanel-Fantastico will not work correctly.
You can read about it here: <a href="http://g30rg3x.com/utf8-database-converter/">UTF-8 Database Converter</a>.

What I do suggest:
First, backup your wordpress database with this plugin: <a href="http://www.ilfilosofo.com/blog/wp-db-backup/">Wordpress database backup</a>
Second, convert the database with UTF-8 Database converter.
Third, enter Fantastico and apply the normal conversion.
It has worked for me smoothly with three differente blogs.