What do I have to consider when backing up a database with millions of entries? Are there any tools (maybe bundled with the MySQL server) that I could use?
Watch out if using mysqldump on large tables using the MyISAM storage engine; it blocks selects while the dump is running on each table and this can take down busy sites for 5-10 minutes in some cases.
Using InnoDB, by comparison, you get non-blocking backups because of its row-level locking, so this is not such an issue.
If you need to use MyISAM, a common strategy is to replicate to a second MySQL instance and do the mysqldump against the replicated copy instead.