Can the Airbus A380 or Boeing 787 land safely without flaps/slats/spoilers or thrust reversers?
Even the largest commercial airliners are able to land without flaps. See a report here where an A380 landed with no flaps. This was at the Auckland, New Zealand airport, where the runway is 3,635 m (11,926 ft) long.
The pilots have information about what speeds they should fly with what amounts of flaps. They simply land at a higher than normal speed. The brakes can end up getting hotter than normal, so they may have to stop and let them cool or have them inspected by emergency services. The tires are designed to deflate with fusible plugs before high temperatures would cause them to blow.
Aircraft are also tested to make sure they can reject a takeoff at high weights (higher than normal landing weights) using no thrust reversers. Here is a video of the 747-8 doing this test.
Specific information can be difficult to come by, and each airline may have their own guidance on the subject. I wasn't able to find anything for the 787, but for the according to one 777 crew handbook I found, flaps up landing was not part of certification:
Basically this means that a demonstration of a no-flaps landing was not required during certification, so no specific guidance appears in the official handbook, and the manufacturer makes no claim that it can be done safely.
None of the Boeing 787 handbooks I found had official procedures for a flaps-up landing either.
That doesn't mean that it can't be done, but pilots are "on their own" so to speak, and the airplane may not be usable afterward.[see note]
But the basic procedure you'd expect them to follow is somewhere along these lines:
[note] "If you can walk away from a landing, it's a good landing. If you use the airplane the next day, it's an outstanding landing."
Any aircraft can land without those devices. I would say that the Gimli Glider is a nice example, with no power it could not extend its flaps/slats.
They are used, as @ratchetfreak notes in the comments, to reduce the touchdown speed and, as a consequence, the runway length needed to reach a stop or taxiing velocity.
To be noted, also, that a safe landing is mostly defined by the vertical velocity at tochdown, usually in the order of 1-3 feets per second. See for example this accident report where it states
Since the vertical component is the relevant parameter for a safe landing, and given that without flaps/slats the forward velocity will be larger than usual, the aircraft will have to approach with a shallower angle than the usual 3°.
Absence of thrust reversers, as you might imagine, will only affect the braking process.