viruses are not living as they do not exhibit many traits that living creatures do (eg. homeostasis, metabolism, growth, asexual or sexual reproduction, etc).
If you consider a virus to only be the infectious particles outside of a cell, that's true. However, that's not even the interesting portion of a virus's existence. It's just a kind of dormant spore.
When a cell gets infected with a virus, one could argue that the original identity of the cell is lost, and the newly reprogrammed cell now *is* the virus, and it is in its active phase. The cell is born again. It is no longer concerned with replicating its original self (or the organism it belongs to), but instead it becomes mainly dedicated to replicating the virus.
There is no doubt that the virus is alive at that point, as it consumes energy and cranks out more spore particles. When the cell bursts and releases the particles, it goes back into the dormant phase until it comes alive again in new cells.
So I'd argue that a virus is alive, but only intermediately. It has the ability to suspend itself into pure information between active states, then reconstitute itself.
It's life, but not as we know it.