Can rhino be reinstalled on a new computer?

Hello,
I had just bought a new computer and am wondering if I can use the same key card I used for my old computer to install rhino on the new computer.

Yes.
Here’s a link to the license agreements with the details:
http://wiki.mcneel.com/rhino/licenseagreements
It’s only one page long.

Here’s the important part:
Robert McNeel & Associates grants you the non-exclusive license to use the Software on any computers owned by you so long as the number of simultaneous users does not exceed the number of licenses you own. If you run the Software on a server, the number of simultaneous users must not exceed the number of licenses you own. Unless otherwise noted on your license key, all licenses are single (1) user licenses. Educational Lab and Not For Resale Lab licenses are thirty (30) user licenses.
Use the Zoo to manage floating licenses.