To what level do phono cartridges age?

Actually moving magnet and iron cartridges should last as long as their styluses regardless of age. The problem with moving coil cartridges is that copper work hardens. The vibrations travel down the fine wire to the point were they are soldered to a terminal which serves as the fulcrum. The wire will eventually break here. Gold does not work harden so theoretically cartridges with gold coils could last a very long time. I have had two cartridges die this way. It does depend on usage.
Some people believe the suspension changes or hardens with age. I do not know if this is the case. I can't tell that it is as the change would be so slow. I have not noticed this in any of my cartridges. If it is true the compliance of the cartridge would drop over time and your resonance frequency would rise. 

I have a 1975 vintage Audio Technica AT 15/20ss which I purchased new.  I have several NOS AT 20ss stylus' in stock and one AT 15ss stylus.  I recently swapped out a not too old stylus for a new AT 20ss stylus and I cannot say that I have heard any differences in performance between any of them other than they all sound far better than the original OEM one I still have.  But that original one has a lot of abusive hours on it, especially since it went through college with me.  What I cannot believe is the condition of all my original records which have been played hundreds or thousands of times through who knows how many wild parties!   I pulled out some old records I have had since the 60's/70's and 80s and they are still pristine :) 

Thanks for the info guys!

The stylus can wear from use. The cantilever, pole piece, magnet, coil, body and terminals are pretty much forever. That leaves the part the cantilever passes through and pivots around, the elastomer bearing. This is the part that can wear or harden over time and at least theoretically affect the sound.

It seems pretty clear to me that the elastomer bearing is the one part most responsible for the fact that every cartridge sounds better as it warms up from playing a side or two. Everything else I can think of from car tires to basketballs does eventually over time lose its elasticity, get hard, and crack. The same would sure seem to be true and put at least some time factor on a cartridge.

In practice however I have yet to run into anyone who has actually experienced this. I have a Stanton 681EEE from 1974 that near as I can tell still sounds the same as ever. All the people I have talked to, if they have any long term stories at all they are like lewm, no problems.

Now you know one thing, whatever you think the fact is I have noticed for many years now and across several different cartridges that they do warm up and sound better after playing a side or two. So I can hear that subtle (if you want to call it that, it sure ain't subtle to me!) a change over 20 minutes. A similarly subtle change over 20 years? Not so sure about that.

Fair to say I think that a cartridge probably does have a shelf life, just in effect a shelf life longer than yours.

In my direct experience, it's a total crap shoot.  I have cartridges that are 40 and more years old that sound wonderful.  And I have some others with similar age that are clearly not what they used to be.  I would hesitate to name names or to say that one type ages more predictably than another (MM vs MC, for example), because I have no data to point specifically at such a conclusion.  The good news is that nearly every one of the vintage MM and MI cartridges I have purchased in the last 5-8 years works fine, with maybe one exception.  (Jury is out on that one.) I would not be afraid to purchase another vintage cartridge, if I had good faith it was in NOS or near NOS condition, in terms of actual hours of use.