Every domain name requires registration and that registration can be made public, or kept private. Most website owners are unfamiliar with this option, simply filling in their contact details and putting ticks in boxes they think appropriate. SERoundTable discussed this issue and whether or not it would affect your search engine rankings.
There are many valid reasons why you would keep your registration details private. One of these is to prevent spammers and the second is to prevent scammers. However, as the SERoundTable post points out, if you are business, then surely you should have all your details public. For many businesses, their details are already in the public domain anyway.
I can see some possible reasons for an online business to keep its domain registration details private, particularly if they are a private company. Depending on where you live in the world, private companies may have less information available to the public.
From an SEO perspective I can see no reason why it should have any affect. Googler JohnMu says that this information has no affect at all. He does question why a business would go private.
If you have a personal website then the private option can give you some protection from some of the domain name scammers that around at present. If you are a business, while you may feel you need the protection it offers, you need to weigh this up against reputation and credibility that open information provides. If you feel the private domain registration may affect your search engine optimization efforts, fear not – it is not a factor.