In terms of being a living, breathing, alive organism, the answer is no. To qualify as a life form, it must have carbon as part of its chemical makeup. It also has to be composed of cells, either unicellular or multicellular. It also has to have a method of energy production, cellular respiration for animal cells and plants, or photosynthesis for plants only. Finally, it must be able to reproduce, either asexually through binary fission or budding, or sexually through mitosis, fertilization, or conjugation.
In living organisms, viruses only meet the last qualification, reproduction. They must invade a host cell, take over its DNA, replicate within the cell, then go on to invade other cells. They has none of the other qualifications of living organisms so some scientists consider them to be nonliving entities.
In computers, computer viruses serve a similar function. They can not exist on their own, so they take over a host computer's files and internal operating system. They slow down the operation of the computer and interfere with it's normal day-to-day processes. The definition remains consistent, even though we are talking about a machine and internal memory drives.
Even though the definition of a virus and computer virus is constantly being reevaluated, currently both are considered nonliving entities. There are those in the scientific community who think that standard should be revised, and that computer viruses reclassified as organisms that possess some of the qualities of living organisms.