Been a bit of debate raging today on the subject of whether or not there is such thing as a Private Cloud. Rich Miller of Data Center Knowledge outlined a response by Jay Fry that says there is such a thing as a "private cloud" in response to Andrew Conry-Murray of InformationWeek and Eric Knorr of InfoWorld, who contend that there isn't.
Generally the debate goes like this; on one side you have those such as Andrew Conry-Murray and Eric Knorr who say (I'm paraphrasing) that the "Cloud" is an offsite infrastructure provided as a service. Or those like Jay Fry and James Urquhart who say "Internet has Intranet. Cloud Computing has Private Clouds. Similar disruption, localized scale."
As for me, I suppose it depends if you classify cloud computing as Internet based computing or the Internet as an infrastructure model. As I've said before I believe cloud computing is a metaphor for the Internet as a infrastructure model, therefore a private cloud is applying that model to your data center, whether it's closed to the outside world or not is secondary.