What is the average lifespan of a phono cartridge?

How long a cartridge will last is a kind of vague question.  More specific reference to components in the cartridge might be necessary.

Stylus shape, stylus composition, crystal orientation, tracking force, record condition, user habits and other factors contribute to the life, or shortening thereof, of a cartridge and, particularly a stylus.

In many cases, a moving magnet or moving iron with a "replaceable stylus" may not have an expiration date.  If the suspension holds up or a suspension is part of the replacement stylus, what is there to wear out that can't be replaced?

Most moving coil cartridges can have a new stylus and even a new cantilever installed of the suspension components and motor are still operational.

I recently had a new cantilever and stylus put onto a 20+ year old Lyra Clavis Da Capo with excellent results.  I will continue to use that cartridge with rebuilds when necessary.  That will continue until there is a more massive failure of the suspension or motor.  

Bpoletti is exactly right. The stylus is what wears out. On MM cartridges, the stylus is 95% of the total price of a new cartridge, and in some cases it’s actually cheaper to just buy a whole new cartridge if you shop around. Stylus profile has a lot to do with stylus lifespan, because of the size of the contact area. A conical / spherical profile will only be good for 300 hours, while a elliptical could go for 500, and a line contact 800 or 1000. Depending on how frequently you play records, you might need to replace the stylus because the bushings become dry and brittle from age before the stylus tip wears out. 

Here’s a question... what does a worn out cartridge look like...and better still...sound like?
if we all agree that just one pass of a worn out stylus will ruin your record, then determining that your cartridge is worn out...is going to cost you a record..or more.
Interestingly, to me, there must be numerous folks who are destroying their precious vinyl, precisely because they are altering the groove with their worn out stylus...and will not even truly realize this...until they play the same LP with a new cartridge...and hear the damage that they done...which is now irreversible.

One side benefit in the design of Decca and London cartridges is they contain no rubber dampers to dry out, if such a thing actually happens in those that do.

When a stylus is worn, or the suspension has begun to fail, it will not track as cleanly as before.  This is first evident on more difficult to track passages, such as when a female vocalist its a not really hard or gets a bit too close to the microphone.  When you start to notice this sort of change, and cleaning the stylus does not cure the problem, it is time for a replacement.  It is NOT the case that slight, occasional mis-tracking from wear will ruin the record; records are not as delicate as some would make them out to be.  

There is no really good way to determine the extent of wear other than listening for it.  Visual inspection is nearly impossible to do right; often a visual check will not show wear or other problems that are quite evident from just listening.