How long does it take for a virus infection to run its course?

Depends on the virus: That depends on which virus you're asking about. The typical common cold last 3-7 days. Influenza (the "flu") is similar, but sometimes lasts longer. Viral gastroenteritis sometimes just lasts for a day or two. There are other viral infections that never "run their course." for example, herpes and HIV are chronic infections that persist for life.

7-14 days for a cold: See http://www.Richmondent.Com/nose-sinus/sinusitis.Php for more information on how to tell the difference between colds, allergies and sinus infections.