You do need antivirus on Windows, but it's not necessary on Mac OS X. No viruses exist in the wild that can run on Mac OS X, and there never have been any, since it was released 10 years ago. The handful of trojans that exist can be easily avoided with some basic education, common sense and care in what software you install:
Hehe hehe, *smirk*.
I wouldn't say you
need antivirus for windows, especially not if it's windows 7, however if one wants to feel safe, sure.
For the mac osx however, like GGJ says here, no virus has been created for Mac osx, other than a proof of concept virus.
That's not to say you wouldn't benefit from having anti viral software, as I believe it covers both worms and trojans, right? - In that case you would definately need it on OS X as well if you want to feel secure.
Edit: You just adviced against getting anti viral software, GGJ, but those do usually protect against spyware, and the other types of malware, that's illadviced, isn't it?