If you spread a virus on purpose, you can certainly be held liable, on both civil and criminal charges. From the standpoint of civil liability, you could be sued by any number of interests ranging from ISP’s to individual users. Your liability would be damages you caused by willfully spreading the virus. In addition, you could be held liable for exemplary or punitive damages for an intentional wrongdoing. Such liability may not be dischargeable in bankruptcy. With regard to potential criminal liability exposure, intentionally spreading a computer virus could be characterized as a crime under any number of circumstances.
You may not even have to be the one who spread the virus to be held accountable. For example, you may created a virus program or let someone use your computer in spreading it. In such situations, there are ways that a prosecutor could try to hold you responsible. You might be deemed a co-conspirator, or someone aiding and abetting the commission of a crime.
It is not clear whether someone could be held liable for negligently spreading a virus. In most situations, it would probably be a stretch to find liability where an end-user innocently spread a virus by unwittingly doing something like opening up an e-mail. In order to establish such liability, it would have to be shown that the user acted unreasonably and thereby fell below the standard of care of a reasonable computer. However, there are presently many “anti-virus” programs on the market that are able to detect and filter out infected e-mails and other communications, so it may only be a matter of time before claims will be brought on the basis that a user fell below the standard of care by not using a virus scanner.