Try these.  I have three jpegs with fully-saturated colours in sRGB, Adobe RGB and ProPhoto RGB.  The colours in the Adobe RGB image are outside sRGB, and those in ProPhoto are outside even Adobe RGB.  On my wide-gamut monitor I can see a difference. 

If your browser is colour managed (which means Firefox or Safari) then you should see a difference in your browser.  Or save the images on your computer and import into Lightroom.  Again, doing that I can see a clear difference. 

sRGB:

Adobe RGB:

ProPhoto RGB:

You say that my three images appear different from one another in Firefox, which they should.  They were created in Photoshop with 100% saturated colours in each of the three colour spaces.  In other words, R, G and B values are 255 or 0, depending on the colour patch.  If you save the images on your machine (right-click in Firefox and "Save Link As...") then the jpegs should look different in Photoshop and if you import them into LR they should look different there, too. 

However, most images don't look different on a wide gamut monitor.  I have two monitors: one wide gamut (larger than Adobe RGB) and one with a gamut close to sRGB.  I've got tens of thousands of raw images, and very few look much different on the two monitors.  It's only when I create artificial images like the ones above that the difference hits you in the face. 

The reason: most pixels in most images are within or close to the sRGB gamut.  Highly saturated colours (outside sRGB) aren't very common in nature.  That's not to say you won't see a difference on a wide-gamut monitor, but it won't be huge (or shouldn't be) in most pictures. 

Which version of Windows? 

The Windows XP photo viewer ("Windows Picture and Fax Viewer") isn't colour-managed, but the Windows 7 viewer ("Windows Photo Viewer") is colour-managed, and should show a difference between the three images. 

I don't use Faststone, but I Googled and found a reference at http://en.kioskea.net/faq/20748-faststone-image-viewer-enable-the-colo r-management-system that suggests you have to explicitly turn on colour-management by checking an "Enable Color Management System" option.  Another Google hit at http://forums.dpreview.com/forums/read.asp?forum=1006&message=34670930 suggested that at the time (2010) some people were having issues with Faststone colour management, but that may have been user error!   

The core operating system isn't colour managed, only applications.  I think that's true of the Mac OS as well, but more apps are colour-managed.

At a low level in the operating system - video driver level, say - it can't really colour manage, as the OS generally won't know whether the data being written to the screen is a photo, what colur space it is and so on.  So (on Windows, at any rate) the desktop itself is not colour-managed.