What is the 'end of the world' in this case? Complete destruction of the planet, every single last human being, or just current civilisation?
Completely destroying the planet itself is unlikely, unless the sun would go. All-out atomic war or an asteroid strike (or gamma ray burst, etc) could really mess things up, but is unlikely to truly exterminate all life. The chance of it being 'just another extinction event' is far greater.
Destruction of humanity is a possibility, but we're very tenacious, and everywhere. Even in the case of a mass extinction event, we're likely to be able to adapt (even though we'd have horrible amounts of casualties and all that). There's 7 billion of us, and we only need a few thousand survivors for re-population / keeping the species going. If 0.00001% of humanity would survive, that'd be 70 000 people right there.
Destruction of current civilisation is a very real possibility, especially because our society is so highly developed. Our trade routes, food supply and energy networks are all very extensive, complex and fragile, and we really can't do well without.
The most interesting idea though: What if humanity transcended it's humanity? By 2030 we could've cured most diseases with Genetics, Nanotechnology and Robotics, and dramatically change what it means to be a human being. By 2040, people might spend more time in virtual reality than in the real world. This would be the best-case scenario 'end of the current world'.
en.wikipedia.org/wiki/Ray_Kurzweil