If my computer seems to be operating correctly, is it safe to assume that it is not infected?
No. “Simple” viruses have a one-hit attack. They will do something like change your system settings or delete all the files off of your computer. Those are usually safer than the sophisticated ones. “Sophisticated” viruses (predominantly spyware, crapware and worms) usually attempt to make your system (and you) believe it is not infected, never alerting you to the behavior that occurs behind the scenes, thereby enabling the virus to propagate itself to other systems and get the largest infestation possible.
And just “propagating” the virus is not the worst of it. Some viruses (trojans) don’t really do anything but sit and wait, listening for a specific command by its author or distributor across the internet. Often these commands are to attack a single computer by making successive hits to that server with garbage data – this is called a DDoS or “Distributed Denial of Service Attack” – and participating in a DDoS is a federal offense. This could be interpreted to mean that you would be responsible for any damage caused to other computers for allowing your computer to be infected with a virus, even if you are not aware of it!