On the c-theorem I have been reading a few papers on CFT and AdS/CFT regarding the c-theorem and I have a few questions regarding c-theorems: 
a) Why is it that the c-theorem is usually considered for only unitary conformal field theories? Are there examples and proofs for the c-theorem for non-unitary conformal field theories?
b) What are the difficulties in understanding the c-theorem in arbitrary dimensions? (I know this has been shown holographically by Myers and Sinha)
c) While I can understand the maths and the physical arguments behind the c-theorem and it seems that the physical interpretation is easy to follow, is there a physically intuitive way to understand why the number of degrees of freedom at low energy scales for a scale invariant theory should always be less than the number of degrees of freedom for the theory at a higher energy scale?
 A: To try to answer b) and c). 
c) For a scale-invariant theory, c is the same in the UV and in the IR, as is the number of "degrees of freedom". c-theorem is a statement about RG flows and scale-invariant theories are fixed points of such flows. The non-trivial statement is that if you have an arbitrary QFT, there is an inequality between parameters of its UV and IR fixed points. And in this context the interpretation is clear -- in the UV you collect all the microscopic details about the theory, so you see all "dofs". In the IR you look only at large-distance behavior and see less degrees of freedom.
b) C-theorems relate IR physics with UV physics. This is something which is very hard to do in full generality. Consider e.g. QCD with no quarks -- in the UV it is free theory of quarks and gluons, and in the IR it is a trivial theory, since it has a mass gap. But we do not know  this from some general fact, but rather from lots of hard work. C-theorems are easier in even dimensions, since there we have anomalies and the powerful tool of 't Hooft anomaly matching condition -- the anomalies should match between the IR and UV fixed points. This is the basis of Komargodski and Schwimmer proof of c-theorem in even dimensions, as far as I remember.
In odd dimensions I think people have tried to use monotonicity of entanglement entropy to relate UV and IR quantities, and try to produce alternative definitions of c. I am not sure if there is a widely accepted c-theorem in, say, 3d. 
Also, note that in 2d and 4d the c-functions are directly related to correlation functions of the stress-tensor in the RG fixed points. In SUSY theories, stress tensor is often a part of a protected multiplet, and this allows one to compute the central charges exactly in many cases.
