Amplifier capacitors
Electrolytic capacitors are well known to pass a small DC current. How much they pass is a complex function of temperature, capacitance, the age of the capacitor, and the DC voltage across it.

This is because the insulating film is formed by electrolysis; as the current flows, it electrolytically deposits an insulator on the anode (which is aluminium : this is the same process as anodised aluminium) and the insulator eventually stops the current flow. 

So for example an electrolytic that has been unused for several years will draw quite a large current (milliamps) for a while, then the current will reduce as the insulator re-forms itself. The capacitor is healing itself.

The result of this is: 


do not use electrolytics in series with high impedances (say, as coupling capacitors between amplifier stages)
do not use them with no (or reverse!) DC across them (they will not heal, and reverse DC will break them down)
Ideally you want 2/3 their rated DC voltage across them to keep them formed (at least 50% anyway)
do not use them in circuits like R-C timer circuits where leakage will change the time constants
remember that at high temperature (usually 85C) their lifetime is rated at 8000 hours - which is only a year!


Tantalums can be a better choice but have their own problems


Don't use them across a high current supply. Across a low current supply they can self-heal too, but across a high current supply they can turn into fireworks...