Computer viruses are not only transmitted over the internet, they can come via a floppy disk, a compact disk or an email. Most software that you receive from reputable companies will have been pre-checked for viruses but you can never be 100% sure. Although designed mainly to cause havoc with businesses, viruses are generally transmitted unintentionally by individuals who have absolutely no knowledge that the virus is on their computer.
The thing about viruses is that they are invisible, so the fact you may not use the internet frequently may reduce the likelihood of receiving and spreading, but the fact is you simply do not know. E-mail is a very common way of transmitting a virus. Beware of anything that you receive unsolicited and never open an attachment unless you know what it is.
The other thing about a virus is that it can lie dormant on your computer for months. That is to say it will be inactive until a particular event occurs, like working with a specific type of document. Many viruses will automatically be transferred on to anyone you have email contact with, and in some cases your entire address book. You will not even know it has happened.
The worst scenario is you could have your hard drive completely wiped clean and would have no way of getting your files back.
Do not be complacent, the fact is if you have a computer you should have some form of anti-virus software, and make sure you keep it updated as there are new viruses every single day of the week.