DMG and ZIP files can't be downloaded automatically

I've got this problem with my iMac. Whenever I clicked on a link to download a .dmg or .zip file, the browser just won't download it. The only way that I can download these file types is by right-clicking the link and select 'Download Linked File As' or 'alt + click' (provided that the link is a direct one that fetches the file). If the link redirects to some other location, then I can't download the files at all.

This problem is plaguing Safari, Firefox and Chrome. All these browsers just can't download these two file types. I have no problems with other file types like, .doc, .pdf, .exe, etc...

Any idea what went wrong and how to resolve this mysterious problem? Thanks for the advise...