The operating systems we use today all have some security holes through which some people are waiting to exploit. These attacks often focus on technologies such as email or open TCP/UDP ports. Combining OS security holes with an always on Internet technology is certainly a dangerous mix.
Today, DSL and cable Internet connections have to be protected by mechanisms such as firewalls to protect the system. The firewall system will offer features such as packet filtering and network address translation (NAT). The firewall can be a third-party software application installed on the system, or it can be a hardware device.
In addition to a firewall, it is equally important to ensure that the operating system you are using is completely up-to-date in terms of service packs and security updates. Today's client systems typically offer automatic update features that will alert you when a new security update is available.
Following a few safety rules, both DSL and cable Internet can provide safe Internet access. We just have to be security diligent.