In reply to:
Dump => tar => some action (copy to some folder or mail the tar) would be a more complete feature.
Basically what you want is:
#!/bin/sh
echo "Content-type: application/x-compressed-gzip"
echo
mysqldump DBNAME | gzip --to-stdout
Although I'm not sure if that content-type is right. But through that script behind a link with a script name like "current_db.gz", and make that program run as a CGI and not have the server treat it as a gzip archive, and the browser will be completely oblivious that the DB isn't a static file but is actually being created/gzip'ed on the fly. :)
D