After downloading and installing new software, is it a good idea to save the file(s) in your hard drive? When purchasing or updating programs, I generally move the exe file from my desktop to my C drive, but then began to wonder if it was really necessary, or if I was just taking up space on my HD.

   Yes, and yes.
   Yes, it is a good idea to save the file to your harddrive and, yes, it probably is just taking up space on your HD.
   I always save the file to my harddrive, but with the easy access that we have to the internet, it usually is not neccesary (because you can always just go on the internet and get it again if you need it).
   The times that it comes in handy to have saved the file to your computer are when you do not have access to the internet, when your access to the internet is slow (like with dialup), when you forget where you got the file from on the internet, and when the website where you got the file from is no longer available.
   The situations when you should not save them to your harddrive are if you do not have much extra space on your harddrive or if it bothers you that you have all of those files just sitting there taking up space.

If it helps, I usually save the downloaded files to a folder on my hard drive that I call "Downloads" - imaginative, isn't it? Under that, I make a further folder for each new thing, as sometimes more than one file is available for download, or maybe I might occasionally want to go back to a previous version after getting the latest. I found this invaluable when buying a new computer, as I installed the old hard drive as a slave to the new one, and there were all my installation files ready for use without the bother of finding them on the internet.