We'd like to generate business based on our customers referring us to people they know who could use our product.
Some questions about this:
One program I found very easy to set up and to start with is Zferral.
I have seen others using this program to sell software products.
The drawback is they charge you 4-16% depending on the plan starting from $79.
I would say it is worth to try if you are selling software, e-books or any high-margin products.
Another one to try is http://www.google.com/ads/affiliatenetwork/.
I've used a few, but if your scale allows it, then using notes on the customer records might suffice. If it's really just a matter of passing on your name, and the customer gets credit (that is, you aren't running campaigns or anything like that) this is probably easiest and simplest.
In terms of the drawbacks of referral fees, it cuts into your profit on the resultant sale. The question becomes whether the cost of the fee is more or less than the cost of customer acquisition through any other methods you have. If you're selling a product with a $200 margin, and your "normal" acquisition cost is $20 per customer, then paying for a lead is only worth about $20.
However, if you're looking at a long-term paying customer (e.g. subscription-based service), then the value of an additional customer may be higher, especially if done as a higher flat fee up-front, or as a lower percentage-based fee for the duration of the subscription.