Video files aren't neccessarily safe.. WMV certainly isn't safe by design and there's plenty of vulnerabilities in various decoders and players. It's not a common vector of infection but it's a possibility. Security software is basicly a waste of time too, I got by without any security software on WinXP for a few years without any issue (unless you count ProcessMonitor as security software) and only stopped counting because I'm back on GNU/Linux fulltime.
I'm more security conscious than most (checking legitimacy and integrity of system files from BartPE, running services with limited priveleges, fixing a large number of the security issues inherent in a default WinXP installation, using a limited user account, running my browser in a sandbox and running unknown code in a VM), but I went a little further than the average user would need to keep their system infection-free.
The problem with antivirus software is that it rarely catches the latest-greatest well-written stuff, and is more of a safety-net for stupidity for the most part. However, your system is only as secure as the software you use on it. If you never update your stuff, or you use software that you know is vulnerable, then you're screwed by default.
Also, Linux ISN'T bulletproof. Only moronic Linux fanboys and people who don't know better actually think that. The reason I'd recommend it for security is because it has such a small share in the desktop market that it's users are rarely targeted and due the open source nature of software commonly used on it, response time for fixing vulnerabilities is often faster than with closed source solutions. Instead of having a single small team of people with access to the codebase, anyone can download the source, fix the bug and submit their solution, and due to the community-driven nature of open source projects there's often quite a number of people interested in fixing bugs.
Finally, no you wouldn't need any antivirus software on GNU/Linux. That's not to say that there aren't viruses out there written for the platform, but they can't (usually) take control unless they're executed as root (there's exceptions, but generally privelege escalation vulnerabilities are considered critical and get patched very quickly). I guess you could write a keylogger with limited priveleges or you could even "rm -rf ~" which could be quite devastating, but the simple fact is that nobody really bothers and these are all things you'd actually have to willingly execute (unless you get exploited via your browser or the like), you don't have 1000 worms out in the wild trying to attack you (and if you're not stupid, failing because you've got all incoming traffic blocked at the router) like you'd have with Windows.