One of the great benefits of the internet is its ubiquity. People and organisations from anywhere in the world can not only find but publish content; contributing to the sum of information available to all of us. Even if it's just a blog...
Just as not everyone speaks English, not everyone writes in English and many languages need characters beyond the standard alphabet of ASCII.
Recognising you have a problem
Web pages that display hex glyphs like this indicate that you don't have the right font to display the underlying character.
Our friend Wikipedia has lots of multi-lingual content and generally includes a warning block on pages that might require non-standard font support:
It's not your fault; your computer just needs an extra font or two to support Unicode characters .
Why hasn't (insert manufacturer, government or standards organisation name) fixed this?
Because it's a big job; if it matters that much to you, consider contributing.
In practice, your computer came with a bunch of fonts chosen by the operating system that will work pretty well for pretty much everything the average user normally needs with local variations for language etc. There are no perfect solutions available, so it makes sense for the mainstream suppliers to concentrate on what works for the mainstream users.
Getting some help
Actually just getting a font that includes the Unicode characters and (possibly) adjusting some browser settings.
There are many free and commercial unicode fonts available, with a variety of coverage and styles. I chose the GNU Freefont . It's not perfect, but it's pretty good. We get three font families FreeSerif, FreeSans and FreeMono - read the project pages for details.
Windows 7: Download the font package and install.
Ubuntu: Already packaged with the OS.
Android: You might be out of luck here. Most methods of installing custom fonts require a 'rooted' device; it might work fine, but it might go horribly wrong - you're on your own here.
(I don't have access to an Apple computer for testing, so I can't comment on those).
After installing the font, test some browsers and adjust as required.
Firefox: Just works
Internet Explorer: Set the default font (Tools, Internet Options, General tab, Fonts button):
Safari: Set the default font (Tools, Preferences, Appearance tab):
See the difference
Here are some fragments of an affected Wikipedia page  before and after installing the unicode fonts.
Another interesting web page that contains samples from many parts of the unicode space (planes in unicode-speak) is here . This shows the incomplete coverage of the GNU fonts - so if you have a specific language need, you might have to find a different font.
Taking one day at a time
Unicode is not a perfect solution; the FreeFont fonts are not perfect, but both are better than doing nothing.
1 Wikipedia article on Unicode.
2 GNU FreeFont project homepage.
3 Wikipedia article used as a sample.
4 Alan Wood's Unicode samples.