I just ordered a Mac that will be shipped with Mountain Lion. Is it possible to install Mountain Lion on my other Macs? Or do I have to buy an upgrade in the App Store?
No. The preinstalled copy of Mountain Lion is not licensed to be installed on additional machines.
From the Software License Agreement (2.A.):
You will have to buy an upgrade in the App Store for your other Macs, however for non-commercial use you can install a single App Store purchase on multiple machines, given all the computers are in your control.