Sure. Most virus infections get cured. We are only in the last 20 years hearing about the ones that have become chronic.

Hepatitis C can be cured in about 30% of cases with a combination of pegylated interferon and ribavirin. It works better for genotypes other than type 1. Unfortunately in North America, genotype 1 is the most common type. Only 15-20% of those type are cured with current treatment programs.

Acyclovir works quite well against chickenpox. In any case, the body has been curing itself of viruses all along with its combination of antibodies and phagocytes. The typical person fights off (and cures) 2-3 viral infections a year. They tend to be adenovirus, rhinovirus, coxsackievirus, and various influenza and parainfluenzas.

I am not sure whether you consider active immunization to be a cure, but ....an ounce of prevention is still worth a pound, you know.