Private registration is good if you're running a dodgy website or if you don't want WHOIS scraping bots taking your personal details and spamming you. There aren't many other perks to private registration to be honest.
Another thing worth pointing out here is that making a domain name private after it has been public for more than a day is useless as your details have already been spidered by domain WHOIS services already and accessible forever.
domain be under my personal name, my business name, or completely kept privateIf your company is actually just an extension of yourself -- i.e. a single person sole proprietorship or something similar -- and you intend to keep it this way, then it doesn't matter.
If you expect to seek outside investors later on, or external investment is at least a possibility, or you might involve partners into the company later on, then all domain names relevant to your service(s) should be registered by the company. If you personally own critical domain names, then this might come up as an issue during the due diligence phase before investment. And if it isn't detected, and you later decide to charge the company a steep fee for use of your domain name, then that will probably be viewed as highly unethical conduct by your partners.
Private registration helps prevent spammers getting hold of your details. Not sure how much of a threat this really is though...
godaddy provide an additional service (or product) that can be added on top of a domain name that you buy from them. (I know they offer this for .com's) This product protects your personal info by making whois type info private.
More info: http://www.godaddy.com/domainaddon/private-registration.aspx I "think" some other registrars may offer this service for free?
I know about Rackspace, you can set the domain contact information to Rackspace address instead of your, unlike godaddy, which charges for this service. Also, you may need a part of the information (email) on whois.net if you want to buy SSL certificate etc.