It is unfortunate that the word  "thinking" has to be used for this process of spontaneous thought production as well as to the willed thinking that occurs when one considers say a problem in geometry. It is in the latter that freedom can be said to lie.

some kinds of thinking:

comparative thinking: the inner gesture here is somewhat rooted in our tendency to let the feelings of antipathy and sympathy be drivers for the thinking (likes and dislikes).  So we experience a thought that is comparative: for example: this post is better or worse than the last post.  The "better or worse than" element arises in the thinking due to the semi-conscious feelings of likes and dislikes.

associative thinking: this is a bit like what Jeff C. described above - one thought lead to another and another and another, through some form of association.

naive willed thinking: this can be related to puzzle solving - we have a task of some kind, something we need to do to resolve an issue, and this is our puzzle which can be purely intellectual (a game of sudoku), or situational (where did I leave my keys), or more dramatic (why is she yelling at me?).

The important part, from a self-observation point of view, is to be able to reflect, post the thinking and the arrival of the thought, on the driver - and by this reflection learn about what impulses caused the thinking activity.

meditative thinking: this is a style of thinking (in Spiritual Science) in which a "theme" is contemplated, perhaps as part of an exercise: thinking about a pencil is the typical example, or  a phrase "all we need is love"

true contemplative thinking: this can be like meditative thinking, but here I am speaking of a higher kind (or more pure) kind of thinking, which has a will element in it that is more single minded as it were - instead of focused on a "theme', contemplative thinking is focused on a particular item, such as the various potential meanings of the word "Our" with which the "Our Father..." prayer is commenced - does it, for example, just refer to all human beings, or does it (can it or should it) refer to all existing beings, visible and invisible?

reverie: sometimes called day-dreaming, this is a kind of associative thinking taking the form of seeking a kind of pleasure - it is the feeling outcome that drives the thinking

worry : here we have a kind of puzzle (in a way), but actually some kind of situation that bothers us which we are obsessed with - again it is the driver (some kind of fear or anticipation) that makes this thinking take its course

rehearsing: here we imagine a coming event, and we prepare for it by rehearsing the event mentally

all these can combine in various ways, according to the situation, for example worry and reverie, and this results from an oscilation of the feelings.

Underneath these kinds of experiences is a kind of natural threefold division in the thinking, which could be characterized as follows: thinking in thinking, feeling in thinking and willing in thinking.  There is also discursive thinking (the inner dialog), and picture thinking (making images), and then empty thinking (which cultivates an openness or contentless state) ...

Aspects of feeling in thinking, includes reactive feelings (seemingly caused by events outside us, such as a driver cutting us off) or cultivated thinking (seeking to be in a feeling state of awe or reverence).  Different reactive feelings and different cultivated feelings effect the arriving of the thought in different ways.

In thinking in thinking was have what is a kind of limb activity that is generally sub-conscious - we are trying to "grasp" the thought, maybe while reading or listening to someone else where we know we haven't yet "understood" something.

self-conscious willed thinking is expressly aware of two will elements: the attention and the intention.   The attention is what we focus on, and the intention is the moral reason we are thinking in the first place.  When we learn to do these, with some skill, we are then on a path to organic thinking and pure thinking.  In my writing http://ipwebdev.com/hermit/liveT.html (Living Thinking in Action, second essay: In Joyous Celebration of the Soul Art and Music of Discipleship) I point out these kinds of thinking: thinking "about"; thinking "with"; thinking "within"; and, thinking "as".

These involve a progression from ordinary naive thinking to organic thinking and then to pure thinking.  The progression is produced by three renunciations, coupled with the intention to love the object of thinking.   The first renunciation involves setting aside antipathies and sympathies, the second all prior related thought-content, and in the third renunciation we replace the centrality of our own I with the centrality now of the object of thinking.   This "thinking on our knees" (Tomberg), allows for "it thinks in me" (Steiner), where the gap between our own I and the essence of the object of thought more and more narrows until in thinking "as" we and the object are united.

Organic thinking is more picture like, and the formation of pictures is done with as much consciousness as possible, because we need the pictures to be as exact as possible (following Goethe's exact sensorial phantasy).  This kind of thinking finds the "thought world" (the ethereal world) to appear as a kind of conceptual picture-like landscape, through which the I moves.  During this "movement" through the "landscape" new thought arises

In pure thinking, we are thinking in pure concepts which have a more abstract character on the one hand, but which are also quite concrete on the other (because they are rooted in a very specific situation or purpose).  One can here, for example, do contemplative thinking on the Our Father and the Prologue to the John Gospel with very interesting results (a dialog ensues between our I and the manifestions of spiritual beings in the ethereal world)

kinds of thought:

these were mentioned above, but can be separated out: daydreams, or pictures while rehearshing; mental pictures of specific objects; abstract concepts about certain feelings or the meaning of certain objects of consciousness or sense awareness; - any experience has its corresponding thought, which is produced by the thinking

the kinds of thought (the product of the thinking) are related to the kind of thinking - one is producing cause and the other the product.  Often the two are inseparable, and can only be distinguished post the activity.  For every kind of thinking, there is a related kind of thought.

thought is manifestation, in a kind of way.  the thinking causes the manifestation of the thought.  In monism we are bringing together that which was always together, but which our consciousness has divided (experience and thought), which is why the producing cause (an experience we are thinking about, with, within or as) seems inseparable from the thought.

the other side of this is that an aspect of the thought is that it is an "expression" of another I.  - the "thing in itself" .   Concepts thought in pure thinking are the ethereal garments of spiritual beings.  as we move from thinking about to thinking as, thinking becomes more and more consciously perceptual.

as our consciousness (soul) is already "spiritual" and of the spiritual world, we have both positive and negative potentials present.   the three-fold double complex can influence the whole process, as can the supersensible element via the conscience (the higher I).   Depending on the qualitative nature of the object of thinking, other beings will participate.  For example: a mother selflessly needing to act in a situation with a child will have an experience of the child's angel in the form of a thought-content as needed for the benefit of the child.  Another way to look at this is to realize that thinkng can be warm or cold.  And it can be excessively one or the other.   Too cold thinking becomes callous and indifferent, and too warm thinking becomes obsessive.   The psychological expression: heart thinking, involves learning to do this warm or cold thinking consciously, and is another way to approach the significance of the "intention".

A very important point is to keep in mind what Steiner points out in "Theory", that there is only one concept of a triangle.   This is true of all "concepts", and if we follow this idea out carefully we can understand much.   For example, Barfield in his essay "Rudolf Steiner's Idea of Mind", points out that our naive conception is that our sense world percepts are shared and our conceptual world percepts are private.  Steiner shows that the opposite is true.  It is our sense world percepts that are private (individual points of view of all objects in space) and our conceptual world percepts that are shared (only one of each concept).

That we seem to think in a kind of private and individualized darkness is because of the demands of the current stage of the evolution of consciousness - we are meant to experience spiritual reality as if we were cut off from it .... trapped in our own mind as it were, and divorced from the Gods ... to overcome this seeming separation, we have to will it - we have to wake up inside and realize that when Christ says in Luke: "the kingdom of heaven is inside you", He means that literally.  All the Gospels references to the kingdom being near at hand or close etc is about this - we just have to decide we want to go there - we have to choose reintegration.   Thinking is the vehicle to do this in the Age of Science.