Maybe not viruses much any more, but definitely worms. (And also some automated malicious servers scattered about the Internet that pull lists of devices with certain ports open from Shodan et al, and then repeatedly attempt to attack/penetrate whatever's on those lists.)

There are several videos available on YouTube, of someone connecting a Win9x/2K/XP machine to the modern Internet, waiting just a few minutes, and then observing (through Process Explorer) the silent introduction of various payloads onto the system.