During a decade in Interactive marketing, I’ve heard a litany of long answers to this question. Too many of them assume “viral” only happens on the Internet, or that “viral” means “short online video clip with some immeasurable entertainment value”. The true reason we call it “viral” marketing is because we notice a message behaving in ways analogous to a biological virus.
Biologically (or pathologically) speaking, “a virus is an infectious agent that is unable to grow or reproduce outside a host. [Viruses] use the machinery and metabolism of a host to produce multiple copies of themselves.” [source] Basically, a virus needs a host to survive and replicate.
For all advertisers, the “host” is the audience. So, consider the audience your only medium. Everything else is a channel of this medium. Television, outdoor, mobile, console games, banner ads, radio, branded USB drives, micro-sites, kiosks, widgets, print, DVDs, podcasts… these are all channels of the audience.
Early adopters of the Internet could see the potential for digital media, particularly the Internet, to revolutionize the way messages spread through an audience.
Harvard Business School’s Jeffrey Rayport coined the term “viral marketing” in a December 1996 article for Fast Company magazine: “Viruses do not spread by chance. They let the high-frequency behaviors of their hosts -- social interaction, email, Websurfing -- carry them into new territories.” [source]
In his 1994 book Media Virus!, Douglas Rushkoff explored the idea of viral marketing, from within the larger idea of a "media virus" (which is essentially a synonym for a meme): “if such an advertisement reaches a 'susceptible' user, that user will become 'infected' and can then go on to infect other susceptible users.”
Take “twoallbeefpattiesspecialsaucelettucecheesepicklesonionsonasesameseedbun” for example:
Consumers have had this run-on Big Mac lyric memorized since its introduction in 1975. It is arguably the most viral message McDonald’s has ever given the English-speaking world, and I’m fairly certain it was neither pitched nor sold as “viral”. Not in 1975.
Which makes me think: perhaps none of our ideas should be pitched or sold as “viral”. Viral is a behavior of the audience, not the ad agency. We can craft a message (in the form of a video, a website, a catch-phrase, or whatever form of “brand experience” we dream up), but we don’t make it viral. What we make are means by which a message can become viral; we help it along, make it “sticky” and “easy to spread”.
To keep things in the parlance of biology, we create the (ideal) conditions through which a virus can become contagious, find adequate hosts, and replicate. To marketers, "viral" is simply another term for word-of-mouth, however enabled by the technology available at the time.
All that said, there is a short and simple answer to the question posed in this post’s title:
All great marketing is viral.