EDIT: I'm moving this to the Discussion section because people seem to not like it (lack of upvotes) and to find the writing unclear. I'd love writing advice, if anyone wants to offer some.
I review parts of the reductionism sequence, in hopes of setting up for future reduction work.
So, you’ve been building up your reductionism muscles, on LW or elsewhere. You’re no longer confused about a magical essence of free will; you understand how particular arrangements of atoms can make choices. You’re no longer confused about a magical essence of personal identity; you understand where the feeling of “you” comes from, and how one could in principle create many copies of you that continued "your" experiences, and how the absence of an irreducible essence doesn’t reduce life’s meaning.
The natural next question is: what other phenomena can you reduce? What topics are we currently confused about which may yield to the same tools? And what tools, exactly, do we have for such reductions?
With the goal of paving the way for new reductions, then, let’s make a list of questions that persistently felt like questions about magical essences, including both questions that have been solved, and questions about which we are currently confused. And let’s also list tools or strategies that assisted in their dissolution. I made an attempt at such lists below; perhaps you can help me refine them?
Why it's tempting to postulate an essence: Organisms seem to come in types. New organisms of the given type (e.g., new ducks) come into existence, almost as though the the type “Duck” had causal power. Humans are able to form mental concepts of "duck" that approximately mirror the outside predictive regularities.
Why it's tempting to postulate an essence: Living creatures act very differently from dead creatures. A recently killed animal doesn’t move, loses its body heat, etc., even though its matter is in almost the same configuration. 
3. Free will.
Why it's tempting to postulate an essence: Humans (among other things) are in fact organized to “choose” their actions in some meaningful sense. We (mostly) choose a single course of action in a relatively unified manner that responds to outside information and incentives. “Choice” also seems like a useful internal concept, but I’m not sure how to describe the details here.
4. Personal identity
Why it's tempting to postulate an essence: People have personalities, plans, beliefs, bodies, etc. that approximately persist over time. Internally, we experience consistent memories that happened “to us”, we choose our own actions, and we anticipate future experiences.
Why it's tempting to postulate an essence: We feel pain. We find ourselves motivated to avoid pain. We sometimes almost feel others’ pain, as when we wince and rub our thumbs after watching someone else smash their thumb with a hammer, and we often find ourselves motivated to avoid their pain as well. We can report verbally on the pain, modify our behavior to reduce the pain, etc.
Why it's tempting to postulate an essence: Mathematics often pops up in science. It’s also “simple”, is at least somewhat culturally universal, is relatively easy to implement portions of in machines, has a nice notion of “proof” whereby we can often formally determine what is true, and can often determine true results without much contact with outside empirical data, and is something aliens might plausibly share with us.
7. Reality / existence / the physical world
Why it's tempting to postulate an essence: Our perceptions are well predicted by imagining a set of fairly stable objects that we can see, touch, turn over in our hands, etc. and that retain their color, shape, heft, and other properties fairly stably over time. At higher levels of abstraction, too, the world is fairly lawful and coherent. 
What lessons for future reductions?
These examples suggest the following heuristics:
A. Even when it really, really feels like there should be an essence, there probably isn’t one.
B. Philosophical questions are just ordinary questions that one is particularly ignorant about; they are not questions about separate magisteria that must permanently be reasoned about in some special way.
C. People expect magical essences in places where there really are interesting empirical regularities. In order to understand those regularities, and to create a new set of concepts that better do the work that our old magical essences intuitions used to do, it is necessary to do real research. Ritual assertions that “It’s all physics” and “there aren’t essences” do not create the needed concepts and anticipations.
D. A reasonable first step, in tackling a new confusion, is to ask the why it feels like there is a question or concept there, and to list the empirical regularities, or cognitive artifacts, that contribute to that feeling.
These heuristics aren't original; Eliezer noted them already in his reductionism sequence (which is very much worth reading). But I suspect that many apply these heuristics more to problems they already understand (“of course free will has no magical essence”) more than to problems we don’t yet understand (“of course there is no magical essence that distinguishes our actual, real world from imaginable physicses/worlds that aren't real").
I'm hoping that reviewing heuristics for reduction, and staring at solved and unsolved problems side by side, may help us with the unsolved problems (which I'll attempt some steps toward in subsequent posts).
 I agree with SarahC’s point that humans seem predisposed to impute essences everywhere. Still, discussions about whether there’s a magical essence “free will” seem to pop up more often than discussions about whether there’s a magical essence “carpet”, “ocean”, “California”, or “female”. I mean, folks are interested in these other questions, and they have discussions about what meaning to use and how much that meaning cleaves nature at its joints, but they don’t generally expect a separate sort of essence that has causal powers and isn’t made out of atoms.
 People unacquainted with modern biology seem often to make predictive errors due to expecting an essence of life. For example, I had lunch the other day with a physics professor from a good university who thought that, even if we could assemble an atom-for-atom duplicate of a person's exact physical state, it might well not act like a person for want of a soul. Another acquaintance was surprised to hear that scientists do in fact believe that a cell assembled in a test tube would act just like a cell assembled anywhere else.
 I'm less satisfied with this unpacking than with the others on the list. Can anyone do better?