... Do I need Norton or other security software?
It is better to ask if you need anything more than what you already have, and to ask just what you mean by "security software".
"Security" is a nebulous subject often cited to justify almost any act, responsible or otherwise. Read more about OS X security here:
On the other hand if you are asking about "anti-virus" software the answer is no. There are no viruses known that affect OS X. None. Most Mac anti-virus software is completely worthless and some of it is harmful. Norton is among the worst.
There are utilities than can detect Windows viruses that can attach themselves to emails. Such viruses cannot harm your Mac. Windows users need to protect their own equipment. If you want to detect Windows viruses that may be present on your Mac you can: use ClamXav. It is available in the App Store and is free.
Beware that use of it, or any software for that matter, requires that you educate yourself lest you use it improperly. Start by reading babowa's link above.
I don't use any either. Never have.