I can answer from the customer point of view - there are couple situations I want to refer service or app to somebody:
1. the service or app is VERY cool, I enjoy using it so much so I want to talk about it
2. I'm getting something for referral and the service is good, so people who I refer won't be disappointed
So I just registered to use dropbox yesterday and found what they did interesting. They create a set of tasks you take to gain more free storage. A subset of which is:
Once you've done that you get more free space. I fine the tutorial step important because if you want people to refer their friends you want them to know about all your cool features. Then you give them something in return.
I definitely agree with Sasha though that the service has to be good/cool before you'll get any referrals.
Take a look at openinviter.org.
It imports a user's contact list from most email services or social networks and allows them to send their contacts message. Install the script on your site, customize it for your needs, and tell your existing members that if they like your service, you'd really appreciate some help in spreading the word.
Offering an incentive can be a double-edged sword. I think just asking folks to spread the word if they like it would be the safest bet...
Use social networks. For instance, you can ask users to twit about your web app. / share on Facebook and in return, give them a small discount, increased disk space or make them eligible for a contest.
Dane and Sasha are right on. Focus on making your application useful to your existing customers. Once you have a rapport with them, approach a couple of them for testimonials. For me, testimonials work. I like to hear that a service I am about to pay money for has rabid fans.
You can also get your best customers involved with setting your future direction. Think of them as an advisory board of sorts. When you do this, those customers become tied to your success and want to spread the word. I had a company do this with me and it made me want to advocate for them since the service was excellent and they listen to my needs. In essence, you are creating super fans for your product.
Would it be a good idea, to let existing+happy customers send gift-vouchers (with a 10% discount) to their friends, to invite them to use the product?