Everyone should be concerned about the security of their computer when connected to the Internet.
The minimal security requirements are:
An up-to-date antivirus software.
Enable the firewall of your ADSL router or install one on your PC.
Another precaution is to secure the open (TCP) ports of your PC. TCP/IP port allows data exchange in the form of packets and as such many malware infections are conducted through open ports.
The following tools will allow you to identify the open ports: