according to this post on strobist flash tubes are usually rated between 1000 and 5000 pops.
This is 1000-5000 full power consecutive pops until the tube starts to lose power.
If you don't use full power the tube will last longer, if you don't subject your flash to consecutive pops the tube will last longer, if you don't let it heat up it will last longer, etc. - and when the tube starts to fail it loses power slowly so it's still useable (but not as good) long after it "failed".
So, in real world usage the flash tube is usually going to last longer than the flash/camera it's in (this is more true for compact cameras that are replaced often and less for pro flashes that photographers keep using for years and years) - but if you abuse your flash it will start to degrade after just a few thousand flashes.