I'd say as long society has the profit-based mentality, we won't ever see the light of stepping on another planet than moon. Humankind will perish within 1000 years.
Even with this profit-based mentality, it's expected to land on mars within 50 years, at
most. Plans are for 2020-2030. Just wanted to clear that up.
Also, it was said about 100 years ago that man will not reach the western frontier in 1000 years. The western frontier being the west coast of america. It was said it was impossible to fly in a heavier-than-air craft. It was said it was impossible for man to go to the moon. Now we say it's impossible to go to another star, or to colonize another planet. With current technology, it's impossible to go to another star unless we throw in all the money we have, and all countries unite. But at the turn of the 20th century it would be impossible with then-technology to build the internet, or build an aeroplane.
Sure, we have problems. We may all die form nuclear war, but that is unlikely. No one wants to fire one, and no one is stupid enough to fire one as of now. We have the problem of space. There isn't enough space for all the farms, and all the houses in the way we have them. But we can build up. Vertical farms are a possibility, even though we have difficulties (I mean like towers with farms stacked on top of each other).
Global Warming is a problem, too. But we're at the tail-end of our fossil fuels. If we continue as now, we will have used them all up in 100 years or so. As they become more and more scarce, they'll become more and more expensive. countries that need to buy oil, gas and coal for their energy will inevitable turn more and more towards renewable fuel sources.
And not just renewable. If we can get thorium reactors well, we will see an increased usage in nuclear power. Thorium is cheaper, since there is more available. the nuclear waste has a half-life of 500 years, not the 500,000 of uranium (although it cannot be used to make fission fuel, like uranium can). India and china are really pushing to get these reactors to work. In southern france, there is a nuclear fusion plant being built. It will be tested in 2016, and should be fully operational in 2020, if all goes well.
In the next 100,1000, 100000, 1000000 years, what will man do? I have no idea. Technologies are advancing massively. Just as we reach the end of Moore's law due to the uncertainty principle, quantum computers are making an appearance. We are learning more every day about long-term space travel from the ISS. As antibiotics are reaching the end of their life, we will see nanotechnology take hold. Humans have been around for around 100,000 years or so. Cities have existed for around 7000 years, probably more. And we have advanced so far. What will the next 7000 years hold? Who knows? But we sure as hell will have colonized another planet by then. Humans are remarkable at finding solutions.