Each serial number entitles you to install Unity on two machines that you have exclusive use of. i.e each license cannot be shared between two people.
If you wish to migrate your license from one machine to another (i.e you upgrade your machine) simply contact us at support@unity3d.com requesting to migrate your license stating the name of the machine you wish to migrate from and include your serial number or the email address you purchased Unity with.
We will then migrate the license across on our activation servers and once you uninstall Unity from the old machine you can then go ahead and install on your new setup.
Joe Robins
Support Team
Unity Technologies
support@unity3d.com
Assuming this applies to the Droid and iOS modules of the indy version too?
No, I don't think you can do that. I am not 100% how this works, but as I know that means that you can only install Unity Pro twice, once on a machine and once on a different machine. The Unity Pro license code than is somehow bound by these two machines. So, the only thing you can do is uninstall Unity Pro on a machine and doing a reinstall on the same machine. That works! But just uninstalling from a machine and installing on a third machine, I don't think it will work. Even if in the end you will still have it installed on two machines.
But, you can write to Unity support any time and ask them to activate your license for a third machine (maybe offering a short explanation about why you need to do that and stating that you will still have it installed on two machines). They will help you out with this. I know someone else who did that!
That's where the fun begins. Theoretically it should be valid, yes. But sometimes it isn't. If it doesn't work, than your only solution is to write or talk to the Unity Support guys.
Assuming this applies to the Droid and iOS modules of the indy version too?
– anon54791079