If you are on a cable or dsl it's more likely that can happen. A dial-up happens less often.
But, to answer your question YES it could happen if you do not have a firewall.
Black Ice is a good resource, read read read.
Or another one that is Free....is Zone Alarm. Not sure of the web site addresses but try the reading. Do a search for these firewall sites.
You can get viruses from ANYWHERE...not just through your emails you receive. You can also get them from http sites you visit.
Safest way is don't open attatchments till you are better secured. And scan with your virus scan.
(I just got something today from someone in Belize. I e-mailed them right away to ask if they had sent something to me, they responded that they DID NOT) THus, I deleted it right away. It pays to ask or trust your self to be careful. I always was too quick to open up these e-mails but there seems to be more of a rash of "viruses" and hoaxes too.
Gosh, I hope I said all that right, if not Sorry. Just do some of that reading assignment LOL
* I am far from a pro*...so this is only a lesson. It takes lots more reading to know for sure. I learn something new each day.
Hope this helps some.