1. I don't think mankind will annihilate itself due to war.
2. I don't think mankind will drain so many resources the earth can't sustain life.
3. I don't think mankind will overpopulate the planet.
4. I don't think mankind will find intelligent extraterrestial life within a thousand years
1. Mankind is not violent, as I said earlier, mankind is one of the animals that can show compassion and mercy even to competitors and other animals. Furthermore, nukes are really not a viable weapon. They tend to be erratic and damages any land you might consider conquering. They are more used as diplomatic leverage. Or as Civ1 said: OUR WORDS ARE BACKED BY NUCLEAR WEAPONS!!!
2. We haven't seen enough proof or damage by resource loss for the world leaders to radically alter the view of resources yet. Mankind will in its current rate of usage seriously destabilize the world balance. We will get more floods, more fires, less ice, different seasons, and different weather. Yet not enough to convince enough people to change ways. Eventually I think we will see with proof what is happening before we have made it completely irreversible. The damage will take centuries to repair, but eventually there will be no permanent harm. Death tolls might reach billions, many nations miight collapse, any things might occur. Yet these are from a view of the earth, barely noticeable. But as with financial crashes, we just don't learn from the past and we might start overusing the resources again, and once more we will have problems. But never will we cause enough damage in enough time.
3. We will simply run out of resources before that. The life span will shorten but not much else since birth rates will go down. From a view of mankind as a whole or from the view of the planet, it will be barely noticeable. Mankind as species might even think it a plus since we will regain some of the daily competition.
4. The closest habitable planet is not close, and we have no way or even a tried idea on how to get there within ten thousand years. Inbetween distance, time, and lack of energy(not enough sun for photosynthesis), it is not a shred possible today. The 16th century people could not even in their wildest dreams have imagined what the 21st century would look like. I do not claim to know the future or even give accurate guesses, but it is harder to leave the solar system, much less reach another solar system.
The largest and most present threat would be a virus that becomes another spanish flu. We travel so much these days and the virus could spread to several continents before symptoms get noticed. Yet it is not likely to kill mankind, between medicine and biodiversity, some might survive.
Another end of the world scenario is what happens when the universes expansion halts. No one knows what happens then, gravity will probably pull everything together into a single point and restart big bang, but this is just a theory as we have no evidence or solid data. Whatever happens, especially if what mentioned happens, the human race must not only leave their solar system, we must leave the universe. And that is probably hard...