How to keep the size of the database reduced?
Don't dump session, cache_*, watchdog table content (make sure to keep the structure).

For watchdog there's syslog replacement.

If you don't need the access logging in Drupal disable that module and dump that table as well.

For huge content driven websites with lots of edits (and revisions) clearing the revision tables from time to time might help too. (e.g. with node revision delete).