Is applying 5 volts to LED dangerous? The Arduino Uno manual (from the kit) instructs to connect a resistor to GND when lighting an LED on the breadboard with the 5V (socket?). The red, green, and yellow LEDs don't light up so brightly... actually they are barely bright enough to detect. Is it safe to apply all 5 volts by connecting the cathode to the ground with a wire? I tried it for a second and it worked... Just don't try it on the blue, I assume that beyond 5V it will explode, it burnt so bright..

Optional: Why does only the blue LED light visibly?
Different color LEDs are not the same.  The are made with different impurities.  And some colors (blue) were really hard to figure out.  So much so that the blue LED inventor was awarded the Nobel Prize!

Consequently, it should not be assume all LEDs operate at the same voltage and current.  As such, when driving an LED with a constant voltage source, derive the proper series resistance for each case. 

Example 1: 

Given a red LED which may have 1.8 volt drop and may need 20mAmps to operate driven by a 5 volt source, we find the proper series resistor to be...


  V = I * R 
  
  5 - 1.8 = 20mA * R 
  
  R = (5 - 1.8) / 0.020 
  
  R = 160 ohms


Example 2:

Given a blue LED which may have a 3.3 volt drop and may need 20mAmps to operate driven by a 5 volt source, we find the proper series resistor to be...


  V = I * R 
  
  5 - 3.3 = 20mA * R 
  
  R = (5 - 3.3) / 0.020 
  
  R = 85 ohms


Your specific LEDs may have different specifications.  The above are only examples.

Go here for more about calculating the proper LED series resistance.

In general, LEDs that are over driven will grow dimmer and not recover.