Current limiting resistor: where is it best to put it
Several reasons to put it on the high side.  Though there is little practical reason to do it.


Its fairly common practice to put the resistor on the high side. You will make other engineers happy because they recognize what they see and understand its behavior. Most schematics are like that and its good practice to be consistent and to conform to standard.
If the anode gets shorted to ground, the LED simply wont come on, regardless which side you put the resistor.  But its not the same both ways if the cathode gets shorted to ground. If the resistor is on the low side and the cathode gets shorted, nothing limits the current through the LED. You dont want the resistor bypassed because you could exceed the LED's current limit and destroy it. That's why putting the resistor on the side closest to the source is a good idea. 
Testing LED's is easier if the cathode is already tied to ground; you wont necessarily have to tie the other probe to the cathode. Might make troubleshooting a tad bit easier. Just because its easier to find anode and ground than it is to find anode and cathode; limited space to put your probes may prohibit squeezing both leads in.
In the unlikely event that you are dealing with transmission line theory (extremely high frequency [Gigahertz] or extremely long distances [kilometers]), you run the risk of exceeding the current limit of the diode. If you put the resistor on the low end. In theory.  This is because the source wont see the resistive load, thereby limiting current, until after its passed through the diode and met with the resistor. That's assuming the reflected signal translates through the diode to the source in the reverse direction at all (I havent thought about it).  Depending on the duration and intensity of that transient, it could destroy the LED. But if current passes through resistor first then current will be limited prior to reaching the diode. I highly doubt you will need to consider that. You would know if its relevant by the circuits purpose. Plus, it doesn't make sense in my book to put an LED on a transmission line in the first place; a generic diode, maybe.


However, there are exceptions, depending on the circuit design.  Suppose for example you used a BJT as a switch to turn on/off the LED. Depending on the design, it may be prudent to put the resistor on the high side, like normal, or perhaps on the low side. It depends on the biasing voltage available, etc. There are just other considerations, is my point. The explanation others and myself have given depend highly on the assumption of a simple circuit design.