When should I use a low ESR capacitor
If the ESR of the capacitor is high relative to the reactance of the capacitor (\$X_C= \frac{1}{2\pi fC}\$) at frequencies of interest, then you might want a low-er ESR capacitor. 

The requirement for "low-ESR" capacitors normally arises in output filters of switching power supplies, where the frequency is relatively high (kHz to MHz). It's less important in mains filters (including the input filter of a SMPS) where a large capacity electrolytic tends to have a proportionally small ESR so that 100Hz or 120Hz ripple is not greatly affected by the ESR. 

ESR also causes \$I^2R\$ heating, which can dramatically shorten the life of electrolytic capacitors (half life for every 10°C rise is a rule of thumb). 

They're also useful in building ultra-low noise analog power supplies, because the low ESR part can reduce the noise with fewer filter stages when you use a high-quality low-ESR  polymer electrolytic rather than alternatives.