I am running LTSpice IV on Windows 7 64-bit; I'm using dual processors with no problems.
If you are going to install it into the "C:\Program Files" folder, you will need to have administrator priveledges.
I chose to install it in a different directory, because Windows 7 is mighty picky about letting programs perform writes to those subdirectories of the "C:\Program Files" folder; and I find it annoying to have to deal with moving things in and out of there. I'd gotten in the habit years ago of creating a number of partitions on my HDD, keeping C: just for the OS, D: for temporary files, E: for the swap file, and F: for programs. Windows 7 doesn't mind if you monkey around with the Program Files directory on another drive.