Electrolytic caps are the ones that change the most. This is due to the forming of an oxide layer on the plates of the capacitor. New electrolyics are supposed to be completely formed during manufacutring but they do change and improve with use.
If an electrolytic cap is unused for long periods of time it must be re-formed. This is not audiophile snake oil, but a well documented subject. Below is some information from Nichicon taken from "Application Guidelines for Electrolytic Capacitors". Even caps in new gear could have been stored for quite some time prior to the equipment being built.
As for film caps, I don't know how much this applies since they don't use an electrolyte.
2-6 Storage Performance
When an aluminum electrolytic capacitor is stored under
no load conditions for a long period of time, its leakage
current tends to increase slightly. This is due to a drop in
the withstand voltage of the dielectric caused by the
reaction of the anode oxide layer with the electrolyte.
When the voltage is applied to the capacitor, the leakage
current returns to its initial level because of the re-forming
action of the electrolyte (called voltage treatment). If the
storage temperature is high, the leakage current will
increase substantially. Therefore, it is desirable to store
capacitors at normal temperature level with no direct
sunlight. A voltage treatment is recommended when using
a capacitor stored for a long period of time. The treatment
for an individual capacitor is accomplished by charging
up to its rated voltage through a resistance of about 1 kW
and applying the voltage for approximately 30 minutes.
When a capacitor is already built into an appliance, the
appliance must undergo aging. In this case, it is
recommended that the input voltage be raised gradually
with a voltage regulator to the rated input voltage of the
appliance.
Generally, if the capacitor has been stored within 2
years in the storage temperature range of 5~35*C, the
capacitor can be used without voltage treatment.
Fig. 2-10 shows an example of the characteristic
change in capacitors that were stored at normal
temperatures.
full document here
