Virality is the answer to the question: "How many new users will each users bring to your site?" This is called a viral loop (represented by K) in the web marketing slang.

The equation is:

K = Invites * Conversion / Time

Somethings can be done to increase how quickly visitors go through this loop of joining and inviting.

Take a look at what Scratchpad did in order to entice you to share:

Social based contest are also a great way to gain lots of new users and give existing users a chance to win.

Appsumo was running a very popular contest (that did have lots of requirements for entry) this past summer in which you could win a Macbook Air for you and your friend: