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.  

Agree with @chakster .  Different stylus profiles have different lifespans.  Also, the construction quality of a stylus can impact lifespan (crystal structure alignment).  The various line contact styles / profiles listed by chaster have a larger contact surface area that spreads the load over the stylus.  This increases lifespan.  A conical cartridge profile has a very small contact area, actually just a point of contact.  These wear very quickly.  

BUT NOT TO FEAR!!!   

Just because some damage might be done to a record due to a worn conical stylus does NOT mean that your records are totally ruined and unplayable.  A new cartridge using a very small line contact stylus or a cart rebuilt by Soundsmith or others using a very small line contact stylus will be tracing the record groove in a different area, typically tracking MUCH DEEPER in the groove.  This area may not have been damaged.  May not have ever even been touched by a stylus.

I recently had Soundsmith rebuild a cartridge using one of their very small line contact stylus / boron cantilever combinations.  When playing some of my collection that was damaged in the early 80s by a worn Shure conical stylus came out clean sounding and like new.  No audible damage or distortion.  The stylus was obviously tracking a "virgin" part of the groove.