What's the easiest method to backup large MySQL database (Gigas of information)?

mysqldump is usually the very best and quickest method to backup a database, as it is something thats shipped with mysql rightaway.

With respect to the database engine if you work with MYISAM or ARCHIVE tables you should use mysqlhotcopy which enables for copying the tables without needing to shut lower MySQL

http://dev.mysql.com/doc/refman/5.1/en/mysqlhotcopy.html