When do the Boeing 737 Next Generation aircraft reach End-of-life?
Airliners aren't given "end-of-life" dates, unlike, say, Windows 95. They also don't eventually become "unsupported", like an iPhone. 

A plane will be kept flying while it's safe and economical to do so. 

In the case of a particular aircraft, that will depend on many things that have nothing to do with the aircraft itself (oil prices, perhaps) that make it uneconomical to operate. 

Older planes are less fuel-efficient, and at a certain point a passenger airliner may be transferred to cargo duties (where fuel is a smaller proportion of the total cost of owning and operating it) and eventually, if no-one wants to keep flying it, it will be retired.

The point at which a plane becomes uneconomical to operate also has to do with how the aircraft is used - an aeroplane that has been through more pressurisation cycles will enter a more expensive regime of checks or maintenance sooner than one that has not (if an aeroplane will need to undergo more extensive checks for fatigue after say 50 thousand cycles, that might be the point at which an operator decides to replace it).

Almost any aircraft can in fact be kept safe to fly (if it were safe to fly in the first place) if you're willing to spend enough money doing so. This is why the comparison with iPhones and operating systems is instructive; probably nobody on earth has enough money to persuade Apple to keep providing iOS updates and manufacturing spare parts for the iPhone 4, but the economics of operating and obtaining spares and doing maintenance on 737s is quite a different matter.

The 737 −600/-700/-800/-900 models are still being produced, and past experience suggests that such aircraft have something like a 30-year working life span. 

You never know however if unexpected events (like an oil crisis, or the discovery that airliners cause serious health issues in law-makers' children) will dramatically change the economic environment in which they operate - that's in the hands of fate.