How long do good speakers last?

I have owned my Apogee Studio Grands full range ribbon system which were made in 1996 and they sound better that the day they were born.  They have never been touched repair wise for any reason. 

So long as they're not damaged electrically, and you keep the cones out of UV light, new, modern drivers will last longer than a lot of us.

As others have mentioned, woofers with foam surrounds may eventually need replacement of the surround.  The life of such surround is usually shortened by exposure to sunlight and air pollution (particularly ozone).  Other kinds of drivers should last longer.  These days, tweeters are not built with magnetic fluid in the voicecoil gap; that fluid eventually dries up.  
I’ve heard many systems that use terrific sounding woofers that have never had to have the surround replaced because they do not employ rubber foam (e.g. pleated paper surround); some of these drivers are more than 60 years old.  The midrange compression drivers in my system are around 73 years old. 

Infinity InfiniTesimal RS 0.1. 1978 I have 2 pairs never touched other than rotating the woofer (4" DVC Watkins) every 5 years or so and cleaning the switch pots. Poly caps will last 100 years and the BR surrounds will last 100 years with just silicone spray every 2-3 years. There are kits for the ribbon tweeters.

45 years old..

Impressive little speakers still fetch a serious price too.. Mag/Aluminum cast speakers cabinets, fitted with hard wood.. and screen diffuser.. 

Regards

My speakers are 32 and performing well. It depends on the components and materials. Foam surrounds tend to go in about 20 years, depending on humidity and temps...rubber surrounds can last much longer, but I haven’t reached the point yet where I can tell you what it is. Any pots can get oxidized at about any time, but most definitely will grunge up at some point.  Good caps can last a really long time, but after 50 years lots of people replace caps in electronics...not so sure about speakers (they see a lot less heat). I replaced the ferro fluid in my tweeters at about the 30 year mark. All else is near mint on them.

Enjoy your new speakers!