I have a notebook hard drive that was formatted with Windows 7. Should I be able to read it on a Vista machine?
Yes, NTFS is readable all the way back to Windows 2000 Service Pack 3*. Some of the newer extensions are incompatible with the older OSes, but you should have no problem on Vista.
Have a look at the Wikipedia article for more information. It's quite helpful in explaining the different versions of NTFS.
*NTFS was around on older versions of Windows, but depending on the version, would not be accessible.