It has been debated that private domain registration may affect your ability to rank in the search engines, due to the fact that you may be a spammer and might be trying to hide something. Many people won’t do it because they think that if you are a legitimate business, you don’t have anything that needs to be hidden from prying eyes.
Well, if you take a look at the signup page for Google Apps, one of their bullet points mentions that they will give you private domain registration to protect you from spam at no extra cost.
So basically, Google thinks that private domain registration is ok. By the way, I’ve used Google Apps domain service, and I think it’s absolutely horrible. No freedom and customer service is non-existant, at least for me it was.