Just curious if it is important to have anti virus for a virtualized operating system I got to thinking, that operating system is actively connecting to the Internet, so I thought maybe it had vulnerabilities.
If you are virtualizing a version of Windows, I would recommend you do use anti-virus software. Although Windows is running in a VM, it still is Windows and is vulnerable to viruses. A good choice of anti-virus software for Windows is Microsoft Security Essentials, which is free from Microsoft. (Note that: "Your PC must run genuine Windows to install Microsoft Security Essentials.")
If you are virtualizing a Linux distro, there is malware for Linux, so I would recommend anti-virus as well. There are several listed on the Linux malware Wikipedia page, including Avast! (Free) and AVG (Free).
If you're running Windows in a VM and it has Internet access, then yes, you should consider running anti-malware software.
VMs attempt to be as much like real computers as possible, so Windows in a VM is just as vulnerable as Windows running on real hardware.
Although it is important to protect a VM from malware and exploits, it might not be quite as important for VMs where you can easily take a snapshot of a clean system and revert to that snapshot periodically (every day, every user logout, after every time going online, after browsing, etc.) Also, the VM might be running on a system that has an active firewall and suspicious activity logging external to the VM (for example: Little Snitch on a Mac can warn you if a VM attempts to connect to some unexpected port number).
Yes, you should run anti-virus software on a VM, and also on your Mac standalone. Macs are vulnerable to viruses, and Virtual Machines can posse a risk to your Mac because it is emulating a virtual environment. I've gotten my fair share of viruses running Crossover for Counter Strike. So if your going to use a VM I highly recommended using one!
You can never be to safe these days...