The way I do it, the number one thing you want is Fans for your Facebook Page, so, I create an app to get people to become Fans of my Facebook Fanpage and the way I've set it up, it is more viral in that it gets their friends etc to become Fans of my Fanpage too.
For instance, I see that you've got a website that gives away a prize every month. You could setup a Facebook Fanpage to market it. Imagine if someone becomes a Fan of your Fanpage, their friends on Facebook will also see that they're Fans of your Fanpage and will want to check it out too. So, they check it out and also become Fans of your Fanpage and it spreads like that.
The difference with just having a Fanpage or having a viral app with a Fanpage is that a Fanpage on its own isn't as viral as one with an app.