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Life as a concept isn't easy to define formally. Any one trait that you might use to define life finds it's exceptions somewhere; for example if life is defined in terms of reproduction, are mules alive?
One widely accepted definition of life is a highly complex and structured organism that takes energy from the environment in order to keep from reaching chemical equilibrium (that is, to keep things moving inside), put another way, to avoid entropy.
Viruses are not even cells, they don't have a metabolism and they do not reproduce by mitosis or meiosis. They just contain genetic code which they attach to an array of organisms' cells.
Their purpose is of course to transmit their genetic code, as all life does. In that sense they can be said to be alive (but think of the mule above), but they do exist at the very limit of what life is defined to be (or what we humans usually think of as alive).
