Google-chrome – Several unicode characters are not displaying on many big sites (like this: ⁠)

There are several Unicode charactes I'm just seeing as boxes. This happens in Chrome only. The Character Encoding is set to UTF-8, but Autodetection doesn't help.

Example: [⁠]

You will only see two square brackets, but actually there is the Unicode Character World Joiner in between. It's a zero-width non-breaking space.

I also put together a little jsfiddle demo. I can't see the World Joiner character, but I can see the Hair Space. (And by seeing it I actually mean I don't see it. You see?)

This also happens when people post some new style emoticons etc.

How can I fix this?

Update:

This happens everywhere (Twitter, Facebook, you name it). I'm not using special fonts or have changed something font-related on my system (Windows 7, 64 bit). Am I wrong assuming this should just work?

Update 2:

This drives me insane. There are still so many characters that are not displaying.

Example (wrapped gift): ?

As you can see, Chrome is not displaying the character by default. Only when I explicitly set the font to Segoe UI Symbol, it does. Why is Chrome not using the font as a fallback automatically?

How can I make Chrome recognize the Segoe UI Symbol font?