With the number of scammers who try to usurp ownership of domain increasing (I got 2 letters for 3 domains last week), it's a surprise that few people really take advantage of private registration for their domain names. However, many people don't know about WhoisGuard or Domains By Proxy and instead leave their domain names exposed with all identifying information intact. It's no wonder I even got a call yesterday about my domain name. In a way, it's nice to know when people are checking on you. In another way, it's something that can be easily abused.
The obvious SEO question still hasn't been addressed though. If you have a private registration, will your rankings be impacted?
According to JohnMu, it typically doesn't impact rankings, so you need not worry if you are already implementing it.
However, if you're a business, why would you hide your identifying information? What does that say about your company? What happens if your web site gets hacked and there's no obvious or working contact form on your site? It'll be hard to get reached by Google or someone else who stumbles upon your site in that case. Thus, while it's a hassle at times to have to worry about your identifying information, losing your rankings altogether due to intrusions can be a lot more costly to your business.
Also, JohnMu suggests that you list valid contact information in your domain. This is actually required by the ICANN, not by Google. I spent a good chunk of last night updating my new address in the 40something domains I own and it was a hassle, but at the end of the day, it's better to do this than risk losing your domain altogether.
Forum discussion continues at Google Groups.