If you want to use it in both OS'es, then yes, you need both versions. Personally, I would stay far far away from Norton on the Mac, it's got a bad reputation for causing trouble. I would look elsewhere for Mac secuirty software. See Joel's post about various Mac products:
Won't 2 different virus scanners on the same machine interfere with one another?
2 running in different partitions "should" not interfere with each other. The Mac still does not "need" a virus scanner if one is reasonably carefull and backs up often. I would recommend not ever accessing a money site such as one's brokerage account or bank via Windows and then not using a virus scanner on the PC side. It is possible that you could arrange your PC work so that only the Mac will go online.
Thanks, Sam. Yours is probably the answer that makes the most sense at this point. Funny, I've gotten a total of four different answers from different sources: Load it on the MAC and it will cover the VM; load it only on the VM; don't need it on either, need it on both. That about covers all the bases.
Well, in my opinion if you are going to run Windows and allow it to connect to the Internet (whether in a VM or its own physical hardware), then you need a Windows virus scanner installed with it. I don't think a Mac virus scanner is necessary yet, but do make sure you keep up with the OS X updates issued by Apple and DON'T install random sofware off the Net unless you get some kind of general concensus from reputable sources that the software isn't some form of malware. And revist the virus scanner issue as time goes on, it's really only a matter of when it will be needed, not if.
I also use Win 7 in Parallels, and run the free MS Security Essentials just for the VM. I suggest keeping the Mac side separate: ie., I use Intego VirusBarrier x6 for Snow Leopard....works well for me.
Parallels 6 comes with a free subscription to Kaspersky AV, though I'm not sure how long it's good for. Personally, I run Avira free version inside my Win VM. I would stay far away from Norton on the Mac side, opting for either ClamXav (a personal fav, though a challenge for the lesser-informed to configure) or Sophos (free version). Be aware that even though OS X 10.6 now has built-in malware protection, many users are seeing where those malware definitions don't auto-update sometimes for up to two or three days rather than daily as Apple claims. See below and others: