What is known about the effectiveness of reliable computing?
While there are some techniques that can be applied to fault-tolerance for all models, how resistant a computational model is to fault tolerance depends on the model. For instance, Peter Gacs has done quite a bit of research with fault tolerance on cellular automata, and he shows that (with a lot of work) you can build fault-tolerant cellular automata.

Von Neumann proved that by using redundancy, you could build a reliable computer out of unreliable components using only logarithmic overhead.

For quantum computation, quantum circuits can be made fault tolerant with polylogarithmic overhead ($\log^c n$ overhead, where finding the correct value of $c$ is still open). Another open question for quantum computation is whether adiabatic quantum computation can be made fault tolerant in a physically reasonable manner (physically reasonable means it is possible that the method leads to a scalable adiabatic quantum computer; for example, you're not allowed to take the temperature to 0 as the size of the computation gets larger).