What is the motivation for developing a "theory of everything"? What is the reason physicists are working so hard looking for a "theory of everything" and trying to unify gravity with quantum mechanics?
Historically, new theories were always developed to explain observed phenomena which couldn't be explained by older theories. This was the case with Newtonian mechanics (movement of astral bodies), with special relativity (constant speed of light), with general relativity (anomalous orbit of Mercury), with quantum mechanics (black body radiation, photoeletric effect etc.). Every time, an hitherto unexplained observation preceded a new theory.
Yet it appears that there are no observable phenomena right now which cannot be explained by our current theories. Moreover, it is expected that situations where e.g. quantum gravity would come into play (e.g. inside a black hole) cannot be observed by us in principle due to either an event horizon in place, or unattainable energies, or the surface of last scattering blocking the view.
I understand there are e. g. a few unexplained effects in superconductors, but it appears highly unlikely quantum gravity is needed to explain them due to the low mass involved.
So why bother looking for a unified theory? And how is a unified theory supposed to be tested, if every phenomenon can already be explained by our current theories?
 A: One reason is, to put it simply, to "put things in order".
The problem with the current state of affairs in theoretical physics (many decades for now) is:


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*There are inconsistencies in applications of quantum theory  that people do not agree on how to resolve (Are there really particles or really only fields? Or really there is only a psi function? what is measurement and how to make it consistent with Schroedinger's equation?)

*There is incompatibility in mathematical descriptions of world between quantum theory and general theory of relativity. This would be kind of acceptable if the theories dealt with different phenomena on a different level, but there are contact points which make people wonder : quantum theory predicts immense number for energy of vacuum, observations disprove that prediction by many orders of magnitude. Also, do gravitational singularities exist in our world and regardless of that, what exactly happens with matter when it gets close to such singularity?
Also, some people hope such unification effort will lead to other great discoveries in theoretical physics, perhaps explanation of the long-standing mysteries in physics. There are other long-standing unresolved questions in physics theory, such as why the electron has 207 times heavier variant and not some other number, why the fine structure constant is 1/137 and not much bigger, and so on. Basically all fundamental unexplained dimensionless numbers in physics.
A: When the heliocentric system became dominant it was not because the geocentric one was falsified, it was because mathematically it was simpler and once accepted it led to new observations that validated it. Even now in planetarium models the mathematics of epicycles are validated as an alternative coordinate system.
When Maxwell unified electricity and magnetism it was not because he was trying to explain unexpected phenomena, he made analogies and predicted new phenomena. It was because he realized that the mathematics was simpler and encompassed disparate physical phenomena, well modeled at that time. The innumerable unexpected predictions for phenomena that lead to the technological world of the end of the nineteenth century and beginning of the twentieth came much later.
The need for people studying the fundamental physics of their time to unify and simplify the mathematical models, is similar to the need of artists to create beauty, a creative expression. 
Unifying electromagnetism with weak interactions has given a beautiful model and extending the unification to the strong interaction one has the standard model.  Trying to unify gravity , all four known forces in one mathematical model, is a natural extension of this creativity.
Will there be unexpected results the way the unification of electricity and magnetism gave the spectacular results of the technology , which together with the discovery of quantum mechanics has led to our present level of technology? It is not known, and it will be science fiction, and I can make a list of science fiction possibilities:
Beware , science fiction:
example: unification through a string theory introduces extra dimensions. Once such a theoretical model is validated the search for large extra dimensions might lead to discovering their existence, and this could have technological repercussions, depending  on how large the extra dimensions are. The velocity of light might stop being a limit, if information can cross through an extra dimension. 
This example is complete fiction, but if one told Maxwell when he was developing his theory that a television could show him what was happening in the Americas he would also consider it science fiction.
The moral of my discourse is that the scientific creativity should be encouraged by society because history up to now shows that crossing frontiers of knowledge in physics has positive repercussions for the society.
