Like the users of Windows, Linux users need to worry about security. While their “market share” is around 1% on the desktop front, on the server and smartphone front, it’s much higher. If you use an Android-based phone, then you’re using Linux. And while it’s true that there have been very few linux malware attacks, it’s still susceptible to attacks from third-party applications (like Flash, Java, or other applications that are installed on the computer). And users are still vulnerable to attacks in places like Facebook.
The layered approach is just as important on Linux, as it is on Windows. In some cases, it’s more important, as you may have servers running that you’re not aware of. And as on Windows, the layered approach starts with the modem/router, moves on to a firewall, and into the computer with separation of users from administrators (including isolating the root or superuser account), antivirus (mainly for scanning windows viruses right now), and online safety habits.