No they do not degrade over time. Not unless they were really poorly made, which is always a risk with these things. Don't get me going on all the crap cables out there giving a bad rep to the whole market.
What definitely does degrade over time though is the condition of the connector at the end of the cable. All of them- power cords, interconnects, speaker cables - should be pulled at least once a year and thoroughly cleaned. Both the cables and the terminals/sockets they go into.
Two other things that will degrade over time: magnetism and static electricity.
How do you magnetize something? Expose it to a strong magnetic field. What goes through your cables? Strong magnetic fields. Over time they become magnetized. Not the whole cable, but regions within. Smearing, grain result.
There are two ways to demagnetize cables. The best/most effective is the Radio Shack bulk tape eraser. (No longer made but available on Amazon) Next best the demagnetizing tracks on the XLO Test and Burn-In CD. If you can't find the Shack there's an overpriced option called the Talisman.
The fix for static electricity is regular anti-static laundry spray sold for about $5 all over the place.
Most people haven't done any of these things in years. If ever. If that's the case, boy do you have a surprise in store when you do!