No you do not, that is one of the best part about owning a Mac. There are no spyware or viruses in the wild for the Mac although there has been a few in the past but has since been patched.
There are no security issues with the Mac which is why its a great platform for home users. I wish I could say the same about Windows but that is not the case you almost need your own IT department to run Windows safely. Windows security is the reason why switched to Linux, Ubuntu to be exact and I love it. There are anti-virus programs out there for the Mac but it’s not really necessary.