Obviously nuclear power plants will continue to fail in the future from earthquakes and tsunamis (Fukushima) and human failure (Chernobyl).

But nuclear power plants will also fail for no apparent reason at all due to reasons explained in detail here:

Hirsch, H., et al. April 2005.  Nuclear Reactor Hazards Ongoing Dangers of Operating Nuclear Technology in the 21st Century.  A report prepared for Greenpeace International.

Failure of  nuclear power plants will lead to even less electricity and ability to load balance the electric grid at a time when this power is most needed due to decreasing electricity from natural gas shortages, droughts & heat waves reducing electricity from hydropower, etc.

Some of these future failures will be due to:

• Aging from irradiation, thermal loads, mechanical loads, corrosion, abrasion, erosion, and embrittlement.   The interaction of these processes increases the danger of a meltdown after a plant is 20 years old (the average age of plants worldwide is 26 years old)
• Climate Change – rising sea levels will flood reactors dependent on ocean water for cooling
• Electric Grid Failure
• Floods
• Droughts and heatwaves – reduces water available to cool nuclear power plants
• Hurricanes, Tornados, and Storms (climate change will increase the number and severity of extreme weather events)
• Maintenance failures – due to poor management, ramping electricity production up too high to make more money
• Regulatory failure – as our financial system begins an inexorable decline from destruction and depletion of natural resources, less and less money will be spent on regulation of all kinds, including nuclear power plant inspections.
• Staffing – inexperienced employees will replace better trained staff familiar with the quirks and issues at power plants
• Terrorism – attacks and theft of nuclear material, potentially leading to EMPs