I've recently received several phone calls from a company that claims my computer has contacted them via the Internet and that it has a "problem". I've had some clients receive the same call, and even my parents have been harassed by these people. If you actually engage them in conversation, they will do everything they can to try and get you to run commands on your computer. I've even actually taken the time to go through the entire script with one of these callers, and if you follow their advice they will actually install and then sell you software that makes your computer more vulnerable to attack.
Something that everyone should know about their computer is that there's no mainstream anti-virus/anti-malware/operating system etc... that "phones home" when it has a problem, so if you receive a call from anyone claiming that your computer has reported anything to them, this is immediately suspect.
Secondly, if you maintain your computer and follow the tips for safe computing (running anti-virus software, running anti-malware/adware software, keeping your system patched, running a firewall, using good wireless security, having a system password, etc.) you greatly minimize the potential for any infection or compromise of your system.
The "bad guys" out there know this, and they know that users are getting more savvy, so they have to figure out new ways to get their hands on your data and/or compromise your system for their zombie army. If anyone ever asks you to go to a website and download anything, unless you know and trust them, I'd do my research first and make sure that they have your best interests in mind... nowadays it seems that threats to your system come not only via email and the Internet, they can come over your telephone!