Resistor selection for LED
While the answers by @Passerby and @MichaelKaras pretty much cover it, there's one more thing to add:


Humans perceive light intensity non-linearly: At very low intensities, we are very sensitive to a even slight variation in brightness. On the other hand, at higher intensity, the unassisted human eye is pretty much incapable of discerning differences in intensity.  

This really interesting graph demonstrates this excellently:
 (source)

Essentially the ability to perceive change in intensity is very high when most of the vision is attributable to the rods of the eye (scotopic vision), and drops very low when the cones are doing the sensing (photopic vision), i.e. at slightly higher luminance.
Less critical but good to know: LEDs illuminate somewhat non-linearly versus current, with the graph dropping off the linear as current increases. This is most noticeable with red.

 (source)


So, long story short: 

The human eye cannot notice even large intensity changes at the higher levels of light that an LED generates at higher currents. Using half or even less than half of nominal rated current (20 mA typical for indicator LEDs, 50mA or more in high power LEDs) will thus work perfectly fine for most indication purposes.

In my designs, 5 mA is my preferred current for all indicator LEDs: Try it, it works great!