Q:

When is using a triple mount a viable strategy? 

Turret mounts have the ability to sacrifice weapon size in favor of their increased number.  

When is this a good thing to do?  Is there a general rule I could adhere to?  
Should I use double or triple mounts?  

A:

Double and triple mounts are great when you plan it out right.  A single huge triple mount turret with 3 large slots offers far more overall DPS than a single huge turret.   Even a single double mount will give you more DPS.   The trade off is the loss of range and increased power consumption.  
However, you can now mix your weapons than relying on a single one.   For instance, putting a leech emitter into one and then two fusion beam emitters into the other slots make for a deadly combo. 
If you rely more on guns and want to go with the particle cannon, you might run into some trouble with the particle cannon as there is an overall limit on the rate of fire produced from a single ship, but with a combo like 2 mass drivers and an ion emitter it'll be super nasty against most things (just watch out for the huge energy requirements).