Check your list of home pages to ensure that it does not include the link for downloading Firefox. If it includes a link that looks something like the following you should remove it.

http://www.mozilla.com/en-US/products/download.html?product=firefox-3.6.8&os=win&lang=da

For details of how to do that see how to set the home page

No downloadurl/link is in my home page. I get the box that says : " Opening Firefox Setup 3.6.8.exe

  You have chosen to open
             Firefox Setup 3.6.8.exe
  Which is a: Binary File
  From: http://mozilla.mirrors.tds.net

Do you wish to save this file?

Another possibility is the file that stores details of your sessions (recent browsing history) is corrupt and is not being updating so still stores details of the download, and tries to access that page whenever you start Firefox.

Use the method shown in the profiles article to open your profile folder. Once you have opened your profile folder close Firefox, then delete sessionstore.js plus if it exists sessionstore.bak from your profile folder. Re-start Firefox to see if you still get the prompt to download the setup file.

I deleted both files while having Firefox shut down. When I opened it again it still open the "Opening Firefox Setup 3.6.8.exe" I've tried un- and re-installing Firefox, however, it doesn't seem to fix it.

Try to delete downloads.sqlite (plus downloads.rdf, if it exists) in the Profile Folder

See http://kb.mozillazine.org/Unable_to_save_or_download_files#Manually_delete_download_history

It didn't help either I'm afraid. It seems that whenever I open a new tab or press links, the setup download begins ..

I am running out of ideas with this one. As a test try creating a new profile, this will show if the problem is with your current profile. See Creating a new Firefox profile on Windows - MozillaZine Knowledge Base

If the new profile works, you can selectively copy some data such as bookmarks and passwords from the old profile. For details of the files that you can copy see Transferring data to a new profile - MozillaZine Knowledge Base

Thanks a ton, Tony! I created a new profile and It's been running smoothly ever since (<- Ever since might be the wrong term since it's only been 20 mins) Anyway, I failed at transferrering the bookmarks, cookies etc. to the other profile, but that's a small price to pay. :-)

Thanks again, Magerz.

PS: Congratulations on your 60th Answer ;-)

You're welcome