Stephen Hawking: We must colonize other planets
Stephen Hawking has been touting colonization of other planets to ensure the survival of the human species, a theme that has existed in Science Fiction since the term was coined. And while the idea may seem a bit eccentric and far fetched, it is doable, assuming a few obstacles can be overcome.
Where would we go?
We need to find an extrasolar planet that exists in the "Goldilocks Orbit", the planet with the ideal orbit of not too hot and not too cold. So far, most of the planets we've discovered have been "Hot Jupiter's", but there could be billions still to discover. Assuming we don't want to make the same mistakes we made with Native Americans, the Aborigines, and other "re-located" cultures, we also need to make sure that the planet isn't currently inhabited or let our ignorance get in the way of what actually constitutes life. Terraforming, the process of turning a barren rock planet into a habitable place to live is probably our best option.
How long would it take?
Here's a nifty little Relativistic Spaceship Calculator you can use to see how long it would take. After about 5 years of spaceship time at a constant 1G acceleration, the spaceship would have traveled about 12 light years distance. At almost 10 years of traveling this speed, the spaceship would have traveled a whopping 150 light years. Even that long of a voyage, it should be generational voyage with planned offspring along the way. What this isn't taking into account is any time necessary for deceleration. Our body's don't take too kindly to sudden stops, seems our organs are a bit wishy washy and like to keep moving when the bones stop.
What would we take?
Imagine packing for a vacation where you're never going to return. You also have to take along all the gas because there are no gas stations along the way. Now throw in your oxygen supply, your food, etc. If you plan on returning, double it. Having to carry everything with you is our biggest road block to putting a human on Mars. For the long journey, relativistically speaking, you don't have to carry 150 years of supplies, just 10 years worth, plus any incidentals once you get there to stay alive. You either have to assume non-replenishing consumables or find some way of acquiring what you need along the way. A self contained bio environment can handle some of the replenishment, but that requires a level of stability we haven't even been able to control here on Earth. Another possibility is building systems that can create CHON food. For fuel, we would have to take a lot of it, discover a really efficient fuel source such as Hawking's suggestion of an Anti-Matter/Matter engine, or be able to scoop up those floating hydrogen atoms along the way using a Bussard Ram Jet.
Conclusion
There are a bunch of issues that we can't even begin to imagine yet. There have been issues of cataracts in astronauts and other effects on the human physiology. We just don't know until we at least try. After a 100,000 years or more, the seeds of humanity would be so different from us because of genetic isolation that we probably wouldn't even be able to recognize them. Not all the seeds would thrive, but some would. Should we reach out to the stars? Absolutely! Should we dedicate an enormous amount of resources to it? Probably not an exorbitant amount, just dedicate enough and perhaps a wee bit more.

