There are Audigy and Live! cards that have some capacitors next to a voltage regulator go bad from the heat they're exposed to. I remember reading of erratic operation in such a case.
But as far as sound quality goes, in general terms, worn out capacitor can have low capacitance which will directly affect the high pass fliter cutoff point. I.e 10µF capacitor that is in spec gives say 10Hz -3db cutoff point, while if it has reached 1µF has it at 100Hz and the result is much thinner sound, especially from headphones or proper speakers capable of actually doing bass freqs.
If the capacitors are on VREF and power supplies, degraded ones can increase noises and interferences that may otherwise be inaudible.