Private clouds are not having the impact many people thought they would, though private clouds are a valid architecture and have value in some enterprise problem domains. However, public clouds are far more common in enterprise deployments.
You see more hybrid clouds than private clouds, but not the hybrids that vendors are selling. Vendors often paint pictures of nicely organized architectures that use hybrid cloud models pairing private and public clouds, but they are very tough to deploy in the real world.
Instead, IT shops are creating their own hybrid clouds to solve their problems. These hybrid clouds are the result of an organic movement driven by the rank-and-file enterprise IT people who simply want to solve their issues using the best technology and approach.