How can I lower the chance of burning out capacitors?
The typical universal input range switching power supply uses a circuit topology much like shown here:



The larger valued high voltage capacitor (highlighted in yellow) has the job of smoothing the rectified DC voltage from the AC power line. 

There are two main failure modes for this capacitor. One is high voltage spikes at the input of the supply that make it in through the common mode choke. Spikes in excess of the capacitor voltage rating can cause damage to the insulating dielectric layer of the capacitor leading to internal shorts. High voltage problems should best be solved by finding the source of such spikes in the power system and taking steps to clamp spikes where they are generated. It can also help to improve the input filter of the power supply, add transient absorbtion devices such as transzorbs or MOVs to the input section and increase the voltage rating of the large capacitor. 

Another failure mode is the internal heating that can occur when current changes in the capacitor reacting with the series resistance (ESR) of the capacitor. This generates heat that can dry out the internal electrolytic materials in the capacitor which causes a decrease in the capacitance. It can also increase the series resistance thus causing additional heating to occur. In the off-line type power supply this capacitor is working at twice the line frequency and the current pulses in the capacitor (known as ripple current) occur as the capacitor is charged on each half cycle and discharged as the rectified AC voltage goes to zero whilst the capacitor is asked to continue to supply current to the output sections of the supply. Several factors can be considered to increase the reliability of this capacitor. First and foremost is to calculate or measure the ripple current during supply operation and make sure it is well within the ripple current range for the selected capacitor. Another parameter to consider is the temperature rating of the capacitor to ensure that it higher than the operating temperature of the power supply. Finally it can be useful to to find capacitors that have a lower ESR value which will lower internal heating for a given amplitude of ripple current.