What hierarchies and/or hierarchy theorems do you know? I am currently writing a survey on hierarchy theorems on TCS. Searching for related papers I noticed that hierarchy is a fundamendal concept not only in TCS and mathematics, but in numerous sciences, from theology and sociology to biology and chemistry. Seeing that the amount of information is vast, I hope that I could ask for some help by this community. Of course, I don't want you to do a bibliographic search for me, but rather I am asking for two kinds of information:


Hierarchies and hierarchy theorems that are the result of your work or the work of your colleagues or other people you are familiar with and you think that are not that well known. This could be for example a hierarchy theorem for an obscure computation model that you're interested in or a hierarchy of specific classes, e.g. related with game theory.
Hierarchies and hierarchy theorems that you deem absolutely necessary to be included in a survey of this kind. This would probably be known to me already, but it would be useful to see what hierarchies you consider more important and why. This could be that of the kind "I deem $PH$ very important because without it we wouldn't be able to do this kind of research" or "Although not so well known, in logic-based TCS we constantly use this hierarchy and I deem it an important tool." . And yes I do believe that people from logic have a lot of hierarchies to mention, however keep in mind we are talking about hierarchies of problems.


I will keep an updated list here:


$DTIME$ Hierarchy
$NTIME$ Hierarchy
$SPACE$ Hierarchy 
Arithmetical (also known as Kleene) Hierarchy 
Hyperarithmetical Hierarchy 
Analytical Hierarchy 
Chomsky
Hierarchy 
Grzegorczyk hierarchy
and the related: Wainer hierarchy
(fast-growing) , Hardy hierarchy
(slow-growing) and the Veblen
hierarchy 
Ritchie's hierarchy
Axt's hierarchy (as defined in Axt63)
The Loop Hierarchy (defined in MR67)
$NC$ ($AC$,$ACC$) Hierarchy  
The depth hierarchy, as defined in Sipser83
Polynomial Hierarchy ($PH$) and the less refined Meyer-Stockmeyer hierarchy (no dinstinction between quantifiers)
Exponential Hierarchy ($ELEMENTARY$)
$NP$-Intermediate hierarchy
(Ladner's theorem)  
The not-so-sturdy $AM$ (Arthur-Merlin)
The $W$ (Nondeterministic Fixed-Parameter) hierarchy and the related Alternating W hierarchy ($AW$-hierarchy) and $W^{*}$-hierarchy (W with Parameter-Dependent Depth)
Counting Hierarchy
Fourier Hierarchy
Boolean Hierarchy (over $NP$) , also equal to the Query Hierarchy (over $NP$)
Hierarchies for property testing, as seen in GoldreichKNR09
The dot-depth hierarchy of star-free regular languages
$BP_{d}(P)$ : The classes solvable by polynomial size branching programs, with the additional condition that each bit of the input is tested at most d times, form a hierarchy for different values of $d$
The time hierarchy for Circuit Complexity
The polynomial hierarchy in communication complexity


Note: If you do not want to be mentioned exclusively, please say so. As a rule of thumb, I will mention both the community and also the specific person that brings new information to light.
The Fourier Hierarchy as defined in "Yaoyun Shi, Quantum and classical tradeoffs."

From the complexity zoo:


  $\mathsf{FH}_k$ is the class of problems solvable by a uniform family of polynomial-size quantum circuits, with $k$ levels of Hadamard gates and all other gates preserving the computational basis.
  
  
  $\mathsf{FH}_0 = \mathsf{P}$
  $\mathsf{FH}_1 = \mathsf{BPP}$
  $\mathsf{FH}_2$ contains factoring because of Kitaev's phase estimation algorithm.
  
  
  It is an open problem to show that the Fourier hierarchy is infinite relative to an oracle (that is, $\mathsf{FH}_k$ is strictly contained in $\mathsf{FH}_{k+1}$).