The Google phone is called Nexus One. It comes with Android OS, 5MP camera, AMOLED screen etc. Unfortunately it has become a developer only phone and is no more available at their official website.
You can however, find a list over current Android devices here. HTC Desire HD is Nice (notice the capital 'N')
yeah the platform is android free and open to many manufacturers and the phone that google actually designed is the nexus one