I think we are not there yet:
http://www.spiegel.de/panorama/lufthansa-airbus-computerpann...
tl;dr: frozen sensors put the plane on a crash course. Plane is saved by pilots completely shutting down the computer system.
We could certainly have software flying a plane tomorrow if we wanted to, at the cost of failure rates several orders of magnitude higher. Humans have the capacity look around, intuit what's going on and what doesn't make sense, and work around it. Software that can detect and understand what to do when 3 things that each occur only one in 1,000 flights, happen simultaneously while 3 out of 10 of the sensor networks are down for maintenance and rare weather patterns are occurring on the route.
We have 100,000 flights per day to cover. Right now, we have lethal accidents roughly monthly, but we have contingency conditions that might plausibly cause a lethal accident a thousand times more often, conditions that are caught, troubleshooted, and successfully mitigated by a human.
But yes, we'll reach a point where the liability of having human beings fly planes vs the sophistication/reliability of an automated system will reach the point where the answer is a foregone conclusion. It's just a half-century away.
More like 10-15 years.
Airliners already spend most of their life on autopilot today. Many (including the Airbus that crashed here) have auto-landing systems[1], too.
Fully autonomous passenger aircraft are being tested[2] in shared airspace since 2012.
[1] http://en.wikipedia.org/wiki/Autoland
[2] http://www.baesystems.com/magazine/BAES_051920/look-no-hands
Autoland needs ground equipment that is expensive to install and has stringent requirements on the surrounding topography that means many airports can not install it. It also takes 2 people's full attention to make the autoland happen in a consistently safe manner, it's not a case of pressing the LAND button and sitting back sipping tea. This video shows a bit of that https://www.youtube.com/watch?v=BMydKAcqKCg
I'm no aviation expert, but isn't that only because the systems in civilian aircraft are decades old?
The state of the art in military drones seems to be autonomous landings on aircraft carriers[1]. The safety requirements for an Airliner are of course much higher than for an UAV, but the underlying technologies seem to be rather mature already.
[1] http://www.theverge.com/2013/7/10/4511476/autonomous-drone-f...
If I could afford it, I would love to make a $10,000 long bet as to when we will see a major airline routinely (1/day) fly a route with > 200 passengers.
I'm saying it won't be later than 2065, but also won't be sooner than 2050.
Where I don't think the technology is moving is on the executive level, which is where having a highly trained and knowledgeable flight crew in the plane is invaluable.
I'm guessing that any trained and qualified pilot of a large commercial airliner (which I am not), can immediately come up with 100 different scenarios for which there is no technology apparent in the next 15 years.
Put another way, in 10 years, 99.99%+ of the time, automated systems will be doing all of the actual takeoffs/flying/landing, but that 0.01% of the time is why we'll keep a flight crew in the cockpit.
Check out:
http://www.newyorker.com/science/maria-konnikova/hazards-aut...
If we automate even more, the problem just becomes worse. We could pull back on automation to keep the pilots alert, but we are increasingly relying on it to optimize resources (air space, fuel, airport take off and landing slots, and ya safety).
And...that's just it. Computers don't get bored. I suffer from some depression also (who doesn't!), but I find that my job keeps me busy enough that I can keep it in check. Imagine being a bit depressed and sitting in a cockpit doing nothing for a few hours at a time.
But this isn't really a huge frequent problem, just one that gets a lot of press.
Until then, having the human pilot capable of overriding the computer is actually a good thing, see danieldk's comment. That the computers should help the humans as much as possible is indisputable, but it's a gradual and hard process to bring the real improvements.
Today, ya, maybe not yet, but we are definitely close. Flying is a hard job on humans, the hours suck, the job can be very monontomous. The problem isn't that the pilots are evil/bad, just that humans are unsuited to these kinds of tasks. Like driving.