On Ubuntu:
First:
sudo apt-get install rsync
sudo apt-get install duplicity
Then:
rsync -avz * myuser@myremote.server.com:/backup/dir/
duplicity --verbosity info --allow-source-mismatch /data/to/backup/securly/also/with/encrypted/transfer/ rsync://myuser@myremote.server.com//backup/dir/for/encrypted/backups/
Finally:
To automate this with periodic execution, use "crontab"-entries, and/or add logic process functionality by using shell scripts.