No computer can be completely free from malware and Trojans. But, to date, there has never been a self propagating virus for OS X.
There are, like on PCs, some simple steps one can take to reduce the risks. Not normally run with administrators permissions, for example and always think twice when presented with a dialogue box.
I have never used an anti-virus programme on my 7 year old iMac. I have never been affected, or infected.