In short – Yes, they can! However, in reality, your plane will only be landing itself around 1-5% of the time. In the industry we call these “Auto-lands”
When do they land themselves?
The aircraft will only be landing itself if the visibility is too poor for the pilots to be able to see the runway just before touching down. It’s pretty rare that the visibility is this low, but in heavy fog, an automatic landing can sometimes be the only option.
Why don’t they just land themselves all the time?
In order to allow aircraft to land themselves, airports have to drastically reduce the flow rate of aircraft. This means longer gaps between landing aircraft, and slower ground movements for departing aircraft.
It’s all in an effort not to distort the ILS* beams that are radiating from the runway to guide the aircraft down. A plane wing or fuselage anywhere near the beam could bend it, and if another aircraft if landing whilst tracking the bent beam in thick fog….the result could have pretty heavy consequences.
Obviously airports nowadays are aiming to be as efficient as possible, squeezing as many departures and arrivals in as possible, so it’s very uneconomical for them to have reduced flow rates when the pilots would be perfectly capable of landing themselves, and it would also be quite pointless.
If anything, it actually places a higher workload on the pilots, controllers, and everyone involved. There’s more to closely monitor, more that can go wrong, and can keep the pilot slightly out of the loop.
Future
I have absolutely no doubt that the future is auto-lands. Whilst a human pilot is currently essential to engage & monitor auto-land mode, I think once the system is finessed and adapted, it’ll be doing a better job than we can. I also think in the next 30 years, pilots will either be totally redundant or down to single pilot ops. Alternatively there may be 1 ‘pilot’ sat in a ground based monitoring room, monitoring multiple aircraft with the ability to manually intervene if required.
*ILS – Instrument Landing System. Basically a set of beams that radiate from the runway. Planes can ’track’ these beams, one vertically, one horizontally, down to the correct touchdown point. It helps guide us down the approach without us needing to be able to see the runway.