If this is a topic that really interests you, I'd suggest searching for papers/reviews/opinions written by Didier Raoult. Raoult is one of the original discoverers of the massive Mimivirus and his work will lead you to some truly fascinating discussions that I couldn't hope to reproduce here.
The main argument for why viruses aren't living is basically what has been said already. Viruses are obligate parasites, and while plenty of parasites are indeed living what sets viruses apart is that they always rely on the host for the machinery with which to replicate. A parasitic worm may need the host to survive, using the host as a source for energy, but the worm produces and synthesizes its own proteins using its own ribosomes and associated complexes.
That's basically what it boils down to. No ribosomes? Not living. One advantage of this definition, for example, is that it is a positive selection (everyone "alive" has got ribosomes) which eliminates things like mitochondria that are sort of near the boundary of other definitions. There are examples on either side of something that breaks every other rule but not this one. Another common rule is metabolism and while that suffices for most cases some living parasites have lost metabolic activity, relying on their host for energy.
However (and this is the really interesting part) even the ribosome definition is a bit shaky, especially as viruses have been found encoding things like their own tRNAs. Here are a few points to think about:
- We have ribosome encoding organisms (REOs), so why can't we define viruses as capsid encoding organisms (CEOs)?
- Comparing viruses to a living organism such as a human is absurd, given the massive differences in complexity. A virus, really, is just a vehicle or genetic material, and would be more rightly compared to a sperm cell. Is a sperm cell alive, or is it a package for genetic material that is capable of life once it has infected/fertilized another cell?
- The really large DNA viruses often create cytoplasmic features called virus factories. These look an awful lot like a nucleus. What is a nucleus anyway? Maybe it's just a very successful DNA virus that never left.
- Viruses can get viruses.
I'll wind down here, but suffice to say that while our current definition may have sufficed for a while, and still does, it is no longer quite solid. In particular, there is a theory alluded to above that eukaryotic life itself actually formed because of viruses. I can expand on this if you like, but here are some great sources:
Boyer, M., Yutin, N., Pagnier, I., et al. 2009. Giant Marseillevirus highlights the role of amoebae as a melting pot in emergence of chimeric microorganisms. PNAS. 106(51):21848-21853 (http://dx.doi.org/10.1073/pnas.0911354106)
Claverie, JM. Viruses take center stage in cellular evolution. 2006. Genome Biology. 7:110. (http://dx.doi.org/10.1186/gb-2006-7-6-110)
Ogata, H., Ray, J., Toyoda, K., et al. 2011. Two new subfamilies of DNA mismatch repair proteins (MutS) specifically abundant in the marine environment. The ISME Journal. 5:1143-1151 (http://dx.doi.org/10.1038/ismej.2010.210)
Raoult, D. and Forterre, P. 2008. Redefining viruses: lessons from Mimivirus. Nature Reviews Microbiology. 6:315-319. (http://dx.doi.org/10.1038/nrmicro1858)
Scola, B., Desnues, C., Pagnier, I., et al. The virophage as a unique parasite of the giant mimivirus. 2008. Nature. 455:100-104 (http://dx.doi.org/10.1038/nature07218)