@2016PARKS"are there airplanes whose computers can (theoretically, and if in control) override any manual input?"
Yes, Airbus 320, 330, 340, 350, F16, Others. Modern Boeings are I think "fly by wire" but I don't know any details.
In the Airbus case the control stick is connected to nothing but computers using electrical connections - the Airbus sticks are not much different from say an Xbox controller. The computers monitor the position of the stick and take movements to be commands to adjust the flightpath. NOT commands to move the control surfaces. A system of computers translates these commands and moves the control surfaces to achieve the demanded flightpath. There is no force feedback, just springs.
Under certain failure conditions the system can revert to Direct Law where the position of the stick is used to command the position of the control surfaces.
In an incident in 2014[1] the captains side stick was accidentally held full down for about 35 seconds. In brief, the computers 'decided' to ignore the command (which would possibly [inevitably?] have resulted in the aircraft breaking up in flight) and maintained a safe flightpath. I forget some of the details but the Airbus has various protections built in. There were two phases to the recovery, I forget the first one but as I recall an overspeed automated protection closed the throttles and applied 1.7g UP which was returning the aircraft towards level flight when the captain removed the camera that was jammed between the control stick and the power-adjustable seat. He had motored the seat forwards. There were injuries.
The airbus goal of going full fly by wire was to improve flight safety. In 2017 there were zero deaths of passengers or crew in Jet Airliners constructed and operated in The West - I forget the exact terminology used. Maybe it's working?
There have been some - "What's it doing now" moments too. Test flight crash in the Mediterranean[2]. As I recall, frozen AoA sensor AND partially-unauthorised/rushed test flight combined to cause the non-passenger flight to crash.
I have the idea that there may be a mechanical-to-hydraulic backup for the rudder controls on some Airbus models but I am not sure.
In all cases I think that all control surface actuators are hydraulic.
https://en.wikipedia.org/wiki/Qantas_Flight_72
"a pair of sudden uncommanded
pitch-down manoeuvres"
No crash but Injuries119 (12 serious)
There is a lot of information about the Airbus FBW systems in the reports about AF447, and on pprune. See posts by GUMS, posts he replies to and replies to his to get started if you don't want to read all of the thousands of posts. There are other good posters too but Mr Gums handle springs easily to mind. He was an F16 pilot and I think test pilot.
[1]
https://www.gov.uk/government/public...-february-2014
[2]
https://www.flightglobal.com/news/ar...-crash-347457/