With an 'always-on' broadband connection it is more likely that a machine can be targeted for attack by someone on the internet. The 'always-on' status means that the machine is likely to keep the same IP address for long periods of time, making it easier for a hacker to spend a prolonged period looking at one machine.
Certainly this leaves the attached device (PC, etc) wide open to the internet. As a minimum a software firewall on any attached PC is necessary to provide security on the connection. A router is a hardware firewall and with a permanently on broadband connection is the quickest and simpliest way to the shut the door on would-be attackers.