There are any number of reasons why someone might want to download Windows 8. Most obviously, if you don't have Windows 8, getting your hands on the operating system via a download is much easier than buying a boxed copy.
Even if you already have Windows 8 on a computer, most manufacturers don't include a copy, making a clean install of Windows 8 pretty much impossible, as well some kinds of troubleshooting that having a copy of Windows 8 available makes a lot easier.
Finally, maybe you just want to give it a try on a spare computer or on a virtual machine. You've seen the prices for Windows 8 and it isn't cheap. There are probably free copies of Windows 8 floating around somewhere, right?
Note: If you do have a copy of Windows 8 (in ISO format or on a disc or flash drive) and also have that copy of Windows 8 installed and working but you've lost your product key, there may be a way to find it. See How To Find Your Windows 8 Product Key for help.
Download Windows 8 the Legal Way
There are five, completely legal ways to download Windows 8.
The first method applies only to students (as well as faculty & staff) with valid .edu email addresses and is pretty straightforward: purchase and download Windows 8 Pro Upgrade from Microsoft for only $69.99 USD. It's as simple as that. You'll get a copy of Windows 8 in ISO format, ready for burning to a disc or transferring to a USB device.
Your third option is to download Windows 7 for "free" as part of a paid TechNet Subscription, costing anywhere from $199 USD to $599 USD per year depending on the tier chosen. This is a professional subscription program available for purchase by anyone, but designed for IT professionals. You get access to full versions of Windows 8, including valid product keys, in addition to software and keys for almost every software and operating system Microsoft has ever created.
A fourth option is the very similar MSDN Subscription program but aimed instead at software developers. This program costs, per year, $699 USD for a new subscription or $499 USD if you're renewing.
As you can see, the TechNet or MSDN programs are anything but cheap. Unless you're an IT professional or software developer that needs access to multiple operating systems, these subscriptions probably aren't cost effective ways to legally download Windows 8.
Your fifth and final option is to download Windows 8 Enterprise... for free. Yes, there's a catch: after 90-days, your computer will begin to shut down every hour and will continue to do so until you replace the operating system. In other words, this is a trial of Windows 8, designed for hardware and software developers to test their products on. This might be useful if you need very short term access to Windows 8 but it's not a long term solution.
If downloading Windows 8 isn't necessary, your other option of course is to purchase a boxed copy of Windows 8 from Microsoft and they'll mail it to you. Popular online retailers like TigerDirect (and others) also sell traditional retail copies of Windows 8.
Note: If you already have a Windows 8 disc or ISO and are only trying to download Windows 8 because you need to install it on a computer without an optical drive, there is a way to get the files from the disc or ISO onto a flash drive. See How To Install Windows 8 From USB for a complete tutorial.
Other "Free" Windows 8 Downloads
Any other free or incredibly inexpensive Windows 8 download you find online is almost certainly illegal, including Windows 8 ISO files you might find on torrent sites. Legal issues aside, these Windows 8 downloads, unlike the official ones from Microsoft, run the very serious risk of containing a surprise or two.
For example, a number of Windows 8 downloads available from unofficial sources are "cracked" versions of Windows 8 installation discs. By "cracked" I mean that they've been changed for one reason or another and could easily contain malware. It would be very unfortunate to install Windows 8 on your computer and be automatically infected with a virus.
Important: Please know that when you pay for Windows 8, what you're actually paying for is the product key used to activate Windows 8. In other words, even if you do download Windows 8 from someone other than Microsoft, you'll still need a valid Windows 8 product key to use the operating system.
Don't Download Windows 8: Replace It
A much better option for those of you with lost or broken, but valid, copies of Windows 8 is to order replacement media. In your case, there's no reason to pay full price for another copy of Windows 8 or risk being infected with malware.
If Windows 8 came preinstalled on your computer, and you did have DVD or flash media but now it's damaged or lost, contact your computer maker for a replacement. Depending on their policy, your computer maker may provide you with Windows 8 media for free or a small fee.
If you legitimately purchased and downloaded Windows 8 from Microsoft, you can download Windows 8 again here, so long as you have your product key documented.
If you purchased a retail Windows 8 DVD, you can contact the Microsoft Supplemental Parts team and request a replacement.
While not a replacement for Windows 8, please know that you also have the option to create a Recovery Drive for Windows 8 using a friend's Windows 8 PC, all for the cost of a small flash drive. Your Recovery Drive can be used to perform all the diagnostic and repair functions that a full copy of Windows 8 can. See How To Create a Windows 8 Recovery Drive for instructions.