You definitely ask a great question and one that's central to many people's first experience with Windows 8. And when I asked about Windows 8 experiences on Facebook, I heard from a lot of people that they were still on Win7 or even earlier versions of Windows. Indeed, one friend said "still on 7, make a compelling case why I should switch!"

I'll let the Microsoft marketing team wrestle with that particular question, and note that once I got over the initial shock of the Tile screen replacing the Start menu, it really does work pretty similarly, especially once you remember that often critical navigational elements only appear when you right-click somewhere on the screen. New = good, right? Well, sometimes, sometimes not.

In terms of your question, the keyboard shortcut to quit an app is the same as it's ever been, so I'm not sure what's going on with your computer. Are you sure you don't have an app running that's remapping your shortcuts?

Specifically, here's a nice list of useful keyboard shortcuts for Windows 8 users:

Charms (the icons that slide in from the right side of the screen)
  •   Win+C: Open charms
  •   Win+Q: Search charm
  •   Win+H: Share charm
  •   Win+K: Devices charm
  •   Win+I: Settings charm

Win8 Search
  •   Win+Q: Search apps
  •   Win+W: Search settings
  •   Win+F: Search files

Insider tip: you can also search by just starting to type in the search pattern from the Tile screen. Try it!

In addition, here are some you can use when you're running Windows 8 applications:
  •   Win+Z: Get to app options
  •   Win+.: Snap app to the left
  •   Win+Shift+.: Snap app to the right
  •   Ctrl+Tab: Cycle through app history
  •   Alt+F4: Close an app (the one you seek)

There are also specific shortcuts related to your Desktop view:
  •   Win+D: Open Desktop
  •   Win+,: Peek at desktop
  •   Win+B: Back to desktop

While we're at it, here are a few bonus shortcuts worth knowing:
  •   Win+X: Open system utility settings menu
  •   Win+PrntScrn: Take screenshot and save to Pictures
  •   Win+Tab: Open switch list
  •   Win+T: Preview open windows in taskbar
  •   Win+U: Open Ease of Access Center
  •   Ctrl+ESC: Start screen
  •   Win+Enter: Open Windows Narrator

Microsoft has a good overview of some of the most useful keyboard shortcuts for Windows 8 here: keyboard shortcuts for Windows 8. There are also other sites where people have experimented to find additional shortcut options, and of course many apps have their own keyboard shortcuts too. What fun, like an egg hunt on Easter morning. :-)