is it safe to delete the file downloaded to install it?
Of course it is safe, it is effectively redundant once installed.
Though I always keep them in a specific downloads folder, with sub folders for the type of program, etc. so I always have a copy just in case I need to reinstall the program. This avoids having to download it again (being on dial-up) and you never know there might be a problem connecting.
While I do the same as David I do think there is a special case.
If you purchase a program for download, especially one where you are also given an activation key then I am especially careful to archive the download file and the activation key. If, at a later time, you need to re-install the program for any reason you may well find that the program has a more recent version for which you would be expected to pay again if you need to re-download.
I hang on to almost all my installer files, they are stored in a folder on a separate partition, and sorted into subfolders, such as “antimalware”, “PC maintenance tools”, “multimedia” “MS packages” etc.
This will facilitate a re-install.
(You don’t want to be swanning around the 'net, looking for an AV to download, on a brand new OS.)
Tell the truth, I’ve got rather too many, and some of them are seriously out of date. And some I’ll probably never use.Heck, some I don’t even remember why I downloaded. The more you keep, the more ongoing maintenance is required to look after them.
Must have a clean up, sometime. 
My downloads folder has 416MB of downloads in 10 sub-folders and I do periodically rummage through it an have a clear out.
Yes,and for me you never really know when something like Kerio 2.1.5 is going to disappear from Last Known Free Version,or for that matter when the site will disappear.
I have no idea where i would get a replacement for my vintage copy of cyberhawk that I thank about re-running from time to time.
It is good to know I am not the only person to rat-hole them!
I just burn the files to a CD once in a while … the archive CD’s are all indexed … not really something that needs cleaning out.
It is rare that I delete a downloaded installation file. Like most of you, I keep them in various folders depending on the type of file it represents.