You're probably viewing the website in the wrong character set.

Try View > Character Encoding > some Japanese encodings, or UTF8 or 16

The website itself should specify the encoding. The default encoding - in Options > Content - is only used if the website doesn't specify an encoding. Maybe the website you're looking at specifies the wrong encoding.

Make sure that you have installed East Asian language support:

• http://en.wikipedia.org/wiki/Help:Multilingual_support_%28East_Asian%29 Wiki: Help:Multilingual support (East Asian)
• http://www.microsoft.com/resources/documentation/windows/xp/all/proddocs/en-us/int_pr_install_languages.mspx?mfr=true - Microsoft Windows XP - Install East Asian language files on your computer

Make sure that you have installed East Asian language support:

cor-el, I guess this is the point. However the wiki article says "In order to display Asian characters in your browser, download and install the Microsoft Global Input Method Editors (IMEs) ... This is the system extension that provides the language support to your English Windows system when you are using Internet Explorer." - does it mean that it will ONLY help in Windows Explorer while I prefer working in Mozilla Firefox?

How would I do this in firefox 4, since there is no view toolbar?

You can access the character encoding via Firefox > Web Developer > Character Encoding

Press F10 or press and hold the Alt key down to bring up the "Menu Bar" temporarily.

I had absolutely no problem until about about a week ago, maybe less. Suddenly, I couldn't see Japanese characters anymore, just the boxes with4 numbers and/or letters inside them. So, has there been some update that interfered with viewing them?

The same thing is happening with Korean characters.

On my other computer, I have Firefox/3.6.17, and it continues to display Japanese and Korean characters correctly.

Try to toggle some of the Boolean gfx font_rendering prefs on the about:config page to disable some features.

Filter: gfx

gfx.direct2d.disabled (f -> t)
gfx.direct2d.force-enabled (f)
gfx.font_rendering.cleartype.always_use_for_content (f)
gfx.font_rendering.cleartype.use_for_downloadable_fonts (t)
gfx.font_rendering.directwrite.enabled (f)
gfx.font_rendering.directwrite.use_gdi_table_loading (t) /questions/782325
gfx.use_text_smoothing_setting (f)

To open the about:config page, type about:config in the location (address) bar and press the "Enter" key, just like you type the url of a website to open a website.
If you see a warning then you can confirm that you want to access that page.
You can use the Filter bar at to top of the about:config page to locate a pref more easily.

Alas, it was the "Constant Guard" security program that was provided by Comcast (my internet provider). As soon as I uninstalled that, the problem was fixed.