Scratch-pad as I become more familiar with the various API classes. Also see:
API: class organization

Starting with Maya 2013, they offered a API Class Taxonomy online, which is all classes arranged according to subject/concept.

This is mainly a place where I can note classes I've used, there are obviously more than what is listed here.

M

Notes:

Maya's base utility classes.

M3dView

"provides methods for working with 3D model views. 3D views are based on OpenGL drawing areas"

MAnimControl

"Control over animation playback and values"

"...a static class which provides methods which determine if an object is being animated, which attributes are animated for a given object and which animation curves are used to animate a given attribute."

Methods include isAnimated, findAnimatedPlugs, findAnimation

MBoundingBox

"Implementation of a 3D bounding box"

MColor

"... used to store values of color attribute."

MDagPath

"Provides methods for obtaining one or all Paths to a specified DAG Node..."

node() : returns an MObject
fullPathName() : Returns string of the full path to the node.
isInstanced() : Returns True\False.

Use MFnDagNode function set to operate on this type.
See:

API: MObject and MDagPath

MDGModifier

"...is used to change the structure of the dependency graph (DG). This includes adding nodes, making new connections, and removing existing connections."

Only usable in scripted plugins. If you call to API commands and want to be able to undo them, you need execute those operations through this class. See this example API: undoing commands.
Used for node creation, deletion, attribute connection, disconnection, attribute addition, attribute removal, node renaming, mel execution, etc.

MDagModifier
Inherits from MDGModifier
"...used to change the structure of the DAG (subset of the DG, focusing on transforms\shapes). This includes adding nodes, making new connections, and removing existing connections.

MDistance

"... provides a fundamental type for the Maya API to hold and manipulate linear data. All API methods that require or return distance information do so through variables of this type."

Great for converting from ui units to system units and vice-versa.

MEulerRotation

"This class provides methods for working with euler angle rotations."

MFileIO

"Methods for opening, saving, importing, exporting, and referencing files."
Also gives query methods for many data items as well (like the scene name, for example).

Closely mirrors functionality found in the mel file command.

MGLFunctionTable

"...is a utility class which provides wrappers for the basic functions in the OpenGL API"

An instance of this class can be obtained from MHardwareRenderer.glFunctionTable()

MGlobal

"Provide methods for selection, 3D-views, time, model manipulation and MEL commands."
Many, many usable methods in here.

deleteNode(MObject) : Delete the given node.
executeCommand(...) : Has a variety of parameter signatures, executes a mel command.
getActiveSelectionList(MSelectionList) : Fill a MSelectionList with what is currently selected (MObjects).
getFunctionSetList (MObject, MStringArray) : Get a list of strings representing the function sets that will accept this object
select(MObject) : Put the given object on the active selection list.
select(MDagPath, MObject) : Put the given object ({{{MDagPath) and components (MObject) on the active selection list.
selectByName(string) : Puts objects that match the give name on the active selection list, can use regular expressions.
setOptionVarValue(string, int) : Set an optionVar with an int value. More similar commands for setting other data types.
sourceFile(string) : Sources a mel script.
viewFrame(double) : Sets the current frame.

MImage

"...provides access to some of Maya's image manipulation functionality."

MImageFileInfo

"...used to describe the characteristics of an image file, such as dimensions, channel count, and pixel format."

MObject

"The generic class for accessing all Maya internal modelling, animation and rendering Objects, collectively referred to as Model Objects, through the API. This includes all Dependency Graph (DG) Nodes, of which Directed Acyclic Graph (DAG) Nodes are a subset."

isNull() : Returns True\False on whether it is a valid MObject or not.
hasFn(MFn.kSomeConstant) : Query to determine if the MObject is comaptible with a given Function Set.function.

Use MFnDependencyNode function set to operate on this type.
See:

API: MObject and MDagPath

MMatrix

"A matrix math class for 4x4 matrices of doubles."

MPlug

"A plug is a point on a dependency node where a particular attribute can be connected."

Similar to the mel commands connectionInfo, isConnected, getAttr, setAttr

MPoint

"This class provides an implementation of a point. Numerous convienence operators are provided to help with the manipulation of points. This includes operators that work with the MVector and MMatrix classes."

MProgressWindow

"...manages a window containing a status message, a graphical progress gauge, and optionally a "Hit ESC to Cancel" label for interruptable operations."

This is like the mel progressWindow command.

MQuaternion

"...provides methods for working with Quaternions"

MScriptUtil

"Utility class for working with pointers to basic types such as int, float and arrays of these types."

Used heavily by Python scripting in the API to make it jive with c++ syntax.
Some good notes HERE.

MSelectionList

"A list of MObjects."

add() : Accepts strings (using wildcards), MObject, MDagPath, and MPlug.
clear() : Empty the selection list.
getDagPath(int, MDagPath, MObject) : For the given index, get the dag path MDagPath and component MObject (if present).
getDependNode(int, MObject) : Get the MObject at the given index.
getPlug (int, MPlug) : Get the plug (attribute) at the given index).
getSelectionStrings(MStringArray) : Gets the string representations of the items in the selection list.
getSelectionStrings(int, MStringArray) : Gets the string representations of the items in the selection list at the given index.
length() Returns the length of the list.

MTime

"Set and retrieve animation time values in various unit systems."

MTransformationMatrix

"...allows the manipulation of the individual transformation components (eg scale, rotation, shear, etc) of a four by four transformation matrix."

MVector

"A vector math class for vectors of doubles."

MFn

Notes:

Wrappers to make accessing common object easier. 'Fn' = 'Function'. They wrapper "functionality". Any class with this prefix is a function set used to operate on MObjects of a particular type.
All MFn classes (except for MFn itself) inherit from MFnBase. The below hierarchy illustrates the class inheritance tree.
The mel command nodeType, via it's apiType flag can be used to query the MFn type of a DAG node, which can then be used to find what type of function set to use.
Bit of craziness: Since Maya stores the Python API in different packages (see API: class organization), it's possible that this inheritance can span multiple packages. For example, this is the inheritance tree for MFnSkinCluster, which as you'll see inherits from two different packages; OpenMaya and OpenMayaAnim:
- OpenMaya.MFnBase (superclass)
  - OpenMaya.MFnDependencyNode
    - OpenMayaAnim.MFnGeometryFilter
      - OpenMayaAnim.MFnSkinCluster (subclass)

MFn

"MFn encapsulates all API Function Set type identifiers used for RTTI in the API."
Meaning, the MFn class holds the constants (MFn.k*) that can be tested against to determine what type function objects can be attached to an MObject. Used with MObject.hasFn()

MFnBase

It has two useful methods:

setObject(MObject) that allows for an MObject to be assigned to the function set after it was created.
object(), which returns the MObject assigned to the function set.

MFnAttribute
"Dependency node attribute function set."

MFnComponent
"This is the base class for all function sets which deal with component objects. Components are MObjects which hold index information for shapes. Examples of these types are mesh vertices (single indexed), nurbs surface CVs (double indexed), and lattice points (triple indexed)."

MFnSingleIndexedComponent
MFnDoubleIndexedComponent
MFnTripleIndexedComponent

MFnDependencyNode
"...allows the creation and manipulation of dependency graph nodes (MObject). Traversal of the dependency graph is possible using the getConnections method."
* MFnDependencyNode() : Creation, no passed in object.
* MFnDependencyNode(MObject) : Creation, passing in an MObject.
* create(string) : (has other signatures, but this one is easiest) : Creates a new dependency node with the given type. The new node is placed into the dependency graph.
* Many methods for node creation, getting connections, name setting, plug (attr) finding, attribute addition and removal, locking & unlocking, query if referenced, query parent namepace, query if name is unique, query if made via plug-in, and more...

MFnAnimCurve
"Create, query and edit Anim Curve Nodes and the keys internal to those Nodes."
*Many, many methods for interacting with animCurves.

MFnExpression
"...used to create, edit, and query expression nodes"

MFnGeometryFilter
"...the function set for geometry filters, the node that is the base class for deformers. Geometry filter nodes include clusters, ffds, nonlinears, user-defined deformers, sculpts, wires and blendShapes. The purpose of the geometry filter is to connect to the geometry that is deformed. The geometry filter is independent of any algorithm that calculates the deformation."

MFnSkinCluster
"...the function set for skinClusters"

MFnDagNode
"Provides methods for attaching Function Sets to, querying, and adding children to DAG Nodes (MDagPath). Particularly useful when used in conjunction with the DAG Iterator class (MItDag)."
* MFnDagNode() : Creation with no dag path.
* MFnDagNode(MDagPath) : Creation based on a dag path.
*Many methods for querying parents, querying children, duplication, node creation, parenting, unparenting, etc.

MFnMesh
"...provides access to polygonal meshes"

MFnTransform
"... provides access to transformation DAG nodes called transforms."
* Creation, transformation, value query, etc.

MFnIkHandle
"This is the function set for inverse kinematics (IK) handles. An ik handle specifies the joints in a skeleton that are effected by an attached ik solver."

MFnIkJoint
"...function set for joints."

MFnData
* "... is the parent class for all dependency graph data function sets. Conceptually, data objects are what flow through the connections in the dependency graph. Each node in the dependency graph has a data block associated with it. The data block holds the data objects for all of the node's attributes (see MDataBlock). The data block is only available during the compute method of a node. A data handle (MDataHandle) can be created to access a particular attribute's data inside of the data block."

MFnMatrixData
*"...allows the creation and manipulation of MMatrix data objects for use in the dependency graph."
*This can be used within user-created nodes to access matrix data.

MIt

Notes:

Used for iterating though data (for looping through things). 'It' = 'Iterator'. They wrapper "iteration". These classes are iterators and work on MObjects similar to the way a function set (MFn classes) does.

MItDag

"Use the DAG iterator to traverse the DAG either depth first or breadth first, visiting each node and, if desired, retrieving the node (as an MObject)."
See:

API: OpenMaya.MItDag

MItDependencyGraph

"Iterate over Dependency Graph (DG) Nodes or Plugs starting at a specified root Node or Plug."
See:

API: OpenMaya.MItDependencyGraph

MItDependencyNodes

"Use the dependency node iterator to traverse all the nodes in Maya's Dependency Graph."
See:

API: OpenMaya.MItDependencyNodes

MItGeometry

"... is the iterator class for geometry data, and can be used to loop over the CVs of NURBS, the points of subds & lattices, and the vertices of polygonal meshes."

MItGeometry(MDagPath, MObject) : Create a new object, passing in the path to the active node (MDagPath) and an MObject of the components to iterate over.
index() : Get the index of the current component.
position(OpenMaya.MSpace.kWorld) : Get the position of the current component as a MPoint.
setPosition(MPoing) : Set the position of the current point.

Good for querying or setting all verts on a mesh at once (for example)

MItMeshVertex

"...is the iterator for polygonal vertices."

MItSelectionList

"Iterate over the items in the selection list."

MItSelectionList(MSelectionList) : Creation, based on a pre-existing MSelectionList
getDagPath(MDagPath, MObject) : Get the path to the current object (MDagPath) and a MObject representing any selected components.

MItKeyframe

"Iterate over the keyframes of a particular Anim Curve Node..."

MPx

Notes:

Used for creating custom plugins. 'Px' = 'Proxy'. They are API classes designed for you to derive from and create your own object types.

MPxCommand

"This is the proxy class for creating MEL commands through the API."

MPxNode

"Base class for user defined dependency nodes."

M

MFn

MIt

MPx

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