Question: I have removed the hard drive from my computer and would like to either install this hard drive in a different computer or transfer the data from the hard drive to some other medium in order to transfer it to a different computer.
Answer: If the hard drive you removed is your system drive (C drive) then it may or may not simply transfer to a different computer and allow you to boot into Windows from it. Windows will not know about the different hardware on the new computer and may not boot. If you were to do a repair installation of Windows after installing the drive but before booting the new computer then it should setup the new hardware and work fine.
If you just want to recover data off this drive then you can install it as an extra drive in the new computer and then transfer the data off of it or simply use it as extra storage. Or you can get an external USB hard drive caddy and put the drive in there and plug it into the new computer. This way you can have your data as a separate backup and also attach it to other computers if needed. If the new computer has a CD or DVD burner then you can burn your data to disk using either method.