user40129: 
I'm not talking about the onboard LED at the Arduino board here.  What those LED's mean, is the LED's we usually plug at the breadboard.

I plugged in a yellow LED and a green LED onto a breadboard.  I wired it up, and noticed something.  Green LED lights up at its full brightness, while yellow LED didn't emit any light.  Tried in another yellow LED, and it seems like it's smoking, which means it's burned.
I'm not using a 220 Ohm resistor or any kind of resistor that time.  I also have no idea why the green LED didn't burn itself, when you plug it directly on 5V and GND.  I'm expecting that the green LED should also be burned, because I think, that's the way how LED's work.
When I plugged the green LED into a 220 Ohm resistor, it did as expected.  It lowered its brightness, of course, because the resistor is resisting some of the electricity to pass on the LED.

user31105: Majenko already mentioned the reason. Maybe it's good to add that different colored LEDs (and even each type/model) should have its 'calculated' resistor.
Find the forward voltage of the LED (differs per type/color), and use the following formula :
V - Vfv = I * R  <=> R = (V - Vfv) / I

E.g. if the forward voltage is 2V and you use a 5V Arduino and want 20 mA:
R = (5 - 2) / 0.02 = 150 ohm

The maximum mA you can find also in the data sheet of the LED.

user4143: 
I'm not using a 220 Ohm resistor or any kind of resistor that time.

Well, there you go then. If you abuse an LED you can expect it to die.

When I plugged the green LED into a 220 Ohm resistor, it did as expected. It lowered its brightness, of course, because the resistor is resisting some of the electricity to pass on the LED.

And the LED was so much happier when you weren't abusing it.

I'm expecting that the green LED should also be burned, because I think, that's the way how LED's work.

It was probably tinged with yellow. And if you left it a while it would get yellower as it got hotter, and then started to fade out, and eventually die.
Different LEDs use different combinations of elements to make the different colours. Different types of the same colour also use different elements. Old fashioned green LEDs are more reliable, though dimmer, than newer ones. They withstand more abuse. But they will still complain after a while.

40129: <blockquote>
  <p>I'm not talking about the onboard LED at the Arduino board here.  What those LED's mean, is the LED's we usually plug at the breadboard.</p>
</blockquote>

<p>I plugged in a yellow LED and a green LED onto a breadboard.  I wired it up, and noticed something.  Green LED lights up at its full brightness, while yellow LED didn't emit any light.  Tried in another yellow LED, and it seems like it's smoking, which means it's burned.</p>

<p>I'm not using a 220 Ohm resistor or any kind of resistor that time.  I also have no idea why the green LED didn't burn itself, when you plug it directly on 5V and GND.  I'm expecting that the green LED should also be burned, because I think, that's the way how LED's work.</p>

<p>When I plugged the green LED into a 220 Ohm resistor, it did as expected.  It lowered its brightness, of course, because the resistor is resisting some of the electricity to pass on the LED.</p>
 31105: <p>Majenko already mentioned the reason. Maybe it's good to add that different colored LEDs (and even each type/model) should have its 'calculated' resistor.</p>

<p>Find the forward voltage of the LED (differs per type/color), and use the following formula :</p>

<pre><code>V - Vfv = I * R  &lt;=&gt; R = (V - Vfv) / I
</code></pre>

<p>E.g. if the forward voltage is 2V and you use a 5V Arduino and want 20 mA:</p>

<pre><code>R = (5 - 2) / 0.02 = 150 ohm
</code></pre>

<p>The maximum mA you can find also in the data sheet of the LED.</p>
 4143: <blockquote>
  <p>I'm not using a 220 Ohm resistor or any kind of resistor that time.</p>
</blockquote>

<p>Well, there you go then. If you abuse an LED you can expect it to die.</p>

<blockquote>
  <p>When I plugged the green LED into a 220 Ohm resistor, it did as expected. It lowered its brightness, of course, because the resistor is resisting some of the electricity to pass on the LED.</p>
</blockquote>

<p>And the LED was so much happier when you weren't abusing it.</p>

<blockquote>
  <p>I'm expecting that the green LED should also be burned, because I think, that's the way how LED's work.</p>
</blockquote>

<p>It was probably tinged with yellow. And if you left it a while it would get yellower as it got hotter, and then started to fade out, and eventually die.</p>

<p>Different LEDs use different combinations of elements to make the different colours. Different types of the same colour also use different elements. Old fashioned green LEDs are more reliable, though dimmer, than newer ones. They withstand more abuse. But they will still complain after a while.</p>
