No. Not anymore.
I still remember about 5 years ago when the machines at work were all hit by the NIMDA virus. I was chugging along happily on my computer when suddenly things started to get very, very slow, and I realized what was happening.
Prior to that, viruses were only activated when you opened the wrong attachment (typically a .scr file). I'm a smart guy, and I knew never to click on those (and a lot of them did come my way). But this one automatically launched as long as your PC was connected to a network drive where the virus executable was stored. And as it launched, it would write itself onto more and more networked resources, and so on...
Nowadays, thanks to a combination of lax Windows security and black magic, if you were to leave an unprotected Windows PC connected to the internet and DO NOTHING with it, you'll find that it gets infected within a very short time - some say minutes, others say seconds. Just sitting there.