There is no simple yes or no answer to that question. See my Mac Malware Guide for information about how to protect yourself, and for information about anti-virus software and what to use if you choose to use it.
There are many forms of ‘Malware’ that can affect a computer system, of which ‘a virus’ is but one type, ‘trojans’ another. Using the strict definition of a computer virus, no viruses that can attack OS X have so far been detected 'in the wild', i.e. in anything other than laboratory conditions. The same is not true of other forms of malware, such as Trojans. Whilst it is a fairly safe bet that your Mac has NOT been infected by a virus, it may have another security-related problem, but more likely a technical problem unrelated to any malware threat.
You may find this User Tip on Viruses, Trojan Detection and Removal, as well as general Internet Security and Privacy, useful:
The User Tip (which you are welcome to print out and retain for future reference) seeks to offer guidance on the main security threats and how to avoid them.
More useful information can also be found here:
While the likelihood of getting a virus is extremely small it's not zero, as was demonstrated by the Java virus. However, while that may be the case it is possible to propagate a virus by forwarding it to someone who can in fact be infected.
FWIW I don't use any anti-virus product outside of ClamAV which runs on my mail server.