I've been using Linux exclusively for ten years. I have had a broadband connection all that time and use the internet constantly. I do not run any anti-virus or anti-malware protection and have had no issues. That is not to say that it can't happen, but the likelihood is so slight and the difficulty in using Linux anti-virus software is such a pain that it is not worth the effort, IMO.
If the threat was credible there would be applications available. Linux users tend to be very security conscious. The same could be said for other Windows practices, such hard drive defragmentation. Yes, you can do it in Linux, but there is no benefit or it is so low that it is not worth the hassle.
This is just an opinion and they vary, but that is what ten years of experience has taught me.