A few years ago, XKCD did a diagram showing the rise and fall of people who had walked on another world [0]
Running slightly to the left of the '50%' mark. Unless Musk pulls his finger out we'll be hitting zero in about a decade.
It doesn't seem likely to me that that is the case. The energy/time requirements to go the closest neighbouring star aren't really that high in the grand scheme of things. Accelerating one ton to c/10 takes 125 terrawatt hours, less than 0.1% of our current annual energy usage. We could then reach the nearest star/expolanet in ~40 years (taking a similar amount of energy to decelerate).
Obviously we aren't putting that much energy into a rocket tomorrow, but give it a few hundred years of technology development and it seems pretty reasonable.
- Accelerate the ship be pointing lasers (or something that accelerates matter) at it from the launch point. Now one doesn't need to carry fuel and the rocket equation no longer applies.
- Use some form of ion engine where we accelerate particles to very high speed relative to chemical rockets. This makes the rocket equation very tame since so little of the mass (relatively speaking) is in propellant.
- Combine the above ion engine with some form of "ramjet" that takes hydrogen we collide with and turns it into fuel. This makes the rocket equation irrelevant since we don't carry our fuel (to the extent that we can get our fuel via the ramjet anyways).
Also as laumars says the 0.1% of annual energy usage was just a point of comparison because terwatts is such a foreign unit to most of us (including me) that it doesn't mean anything by itself.
The first rule of rocketry: For every ton you fire up add 10 tons to what you fire up.
There is a reason space is hard and that is that every ton you launch will require fuel to get into orbit. And now you have to accelerate the fuel for the majority of the way too so you need more fuel. But that also needs fuel ... etc.
Shooting up 0.1% of our annual energy usage will require an exponential amount of energy to get up.
The biggest rocket I ever build in KSP weighed in at 500'000 tons. With a 1 ton payload it only achieves about 250km/s acceleration. That's less than c/1000.
The Saturn V weighs 3'000 tons and has significantly less thrust (though NASA engines outperform KSP engines).
It's simply not realistic to achieve unless you manage to fire up the mentioned 0.1% of our current annual energy production PER ton of weight.
Firstly, technologically advanced species have the ability to modify their own bodies. We already do this with great success and we're barely a few generations into the era of washing our goddamned hands before doing surgery. Additionally you have to consider the difference between individuals, species, and civilizations. Can intelligent robots carry on a civilization? There doesn't seem to be any good reason why they couldn't. And once you are there, then it doesn't matter whether or not it takes 10 years, 100 years, 10,000 years, or even a million years to travel from one star to another. Intelligent, conscious beings who carry our civilization into the stars could indeed do so successfully. Even if they take many thousands of years to hop from star to star and even if they take thousands of years to build up a civilization (on a planet or in orbit of the star using resources from the stellar system) that is then in a position to send out more voyages across the stars. Even then the result will be a massive, sprawling network of our civilization spread across countless stellar systems within a time frame that's a blink of an eye in cosmological terms.
If it took 10 million years for a voyaging vessel to land, settle, grow, and send out only 2 voyaging vessels (and then stop voyaging) then they would colonize a million worlds in 100 million years. In only 400 million years they would have colonized the entire Milky Way.
The fact we don't see the galaxy teeming with life is either 1) intelligent life inevitably evolves rapidly into something unrecognisable 2) we are unique, and not just in our galaxy. Once you hit galactic scale civilisation, neighbouring galaxies don't take long 3) we are part of that expansion