There is a log of confusion about what viral marketing really is. It's your typical scenario of the six blind men trying to describe an elephant. In general I think the following term best describes viral marketing:

Viral marketing describes any marketing or product strategy that knowingly or unknowingly uses individuals to pass a marketing message to others in their social network, who in turn continue spreading the market message. The "marketing message" can be used to create brand awareness, achieve other marketing objects (such as product sales), or simply encourage the use the product, vehicle or service used to deliver the message. This self-replicating viral processes takes advantage of a one-to-many infection ratio and has the potential of achieving exponential growth in the message's exposure and influence.

I have found that viral marketing can take one of three slightly different forms:

• Viral Marketing as Marketing Strategy
  This form of viral marketing involves creating branding awareness through generally available social media marketing channels (such as video, email, social media applications, i.e.).  This type of viral marketing can be exploited by any organization wishing to promote its products or services and usually takes the form of a marketing strategy, campaign or promotion. Creating a extremely funny video and using YouTube to spread your marketing message is probably the simplest example of this (see examples).  Creating a simple financial incentives for existing users to recruit new users is another example of viral marketing as marketing strategy. The success of these strategy depends on understanding customer behavior. For example, it is a known fact that users share humorous content (See Stats), it is also a known fact by people are motivated by money. When employing this strategy make sure you are exploiting known user patterns and not the exception.
  Video Examples: Idea Viral Video, Audio Viral Video, Snicker Kiss Viral Video, Skittles Rabbit Video
  Social Media App Examples: Burger King Ditch 10 Friends,
  Offline Examples: Burger King Last Wallet
• Viral Marketing as Product (a.k.a. "Inherently Viral" Products)
  This is based on the idea that viral marketing can be a fundamental product design discipline and that some products or services are "inherently viral" in nature. Products in this category generally spread each time the product is used. In fact, the use of the product is instrumental to its spread. This type of virality is usually reserved for social media (RockYou, Slide) and peer-to-peer messaging apps (Hotmail, Skype), although you could argue that services like PayPal (sending/receiving money) and vFlyer (classified ad syndication) also spread with general use - so potentially certain ecommerce applications approach this bar. If you are fortunate enough to have a product in this category, great, if not read on.
  Web Services Examples: PayPal, vFlyer
  Social Media App Examples: RockYou, Slide
• Viral Marketing as Product Feature
  I would however argue that adding certain features can indeed make your product or service more (or less) viral.  Hotmail's footer at the bottom of outgoing emails, Amazon.com's introduction and use of affiliate programs, RockYou's and YouTube's use of widgets on MySpace, Linkedin's and Plaxo's ability to import your address book are all good examples of viral features, without which these services might not have been as successfully. I agree with Andrew Chen that "no single product feature determines the viral success of a business" but viral features help and have an additive effect on the overall effectiveness of even the most viral products. I will probably dedicate a post in the near future a comprehensive list of these viral features.

Writing blog posts is time consuming, so I don't always have the luxury of including as many recent examples as I would like to. If you have any good examples, please share (just comment your example) and I will add them to my post.