systemctl disable <service>
If you are not using systemd (Ubuntu 14.10 and earlier) use:
update-rc.d -f <service> remove
The following command will give you a list of all services on your machine:
service --status-all
Example disable Nginx
systemctl disable nginx
// reenable
systemctl enable nginx
For more details, see enabling-and-disabling-services and for the very long answer see this post (as already mentioned by @muru).
For more details, see this post on Digital Ocean and the man page for systemctl.