Part I

I will give an answer focused on STEM field Ph.D.
programs in the US.

Pros:

Professor Career. A Ph.D. is nearly essential for a
career as a professor. If you want such a career,
then about have to get a Ph.D.

Learning. A Ph.D., both in your coursework and your
independent study, can let you learn much more about
your field. Some of what you learn might be quite
powerful and valuable later in your career,
especially if you want to be an entrepreneur and
found a business where some powerful, valuable
'secret sauce' technology will be a big advantage
for the business.

Jobs. Some employers will pay extra for a Ph.D.
Jobs in US national security, working for the
Federal Government directly or work in the
'military-industrial' complex are common examples.

Cons:

(A) With a Ph.D., working for someone without a
Ph.D. can be awkward. Why? Because most
organizations still want to have a hierarchy much
like a Ford plant 100 years ago where the supervisor
knew more and the subordinate was there mostly just
to add muscle to the thoughts of the supervisor.
Then a subordinate who knows more can be a threat to
the career of the supervisor. Related phenomena
include 'goal subordination' in organizational
behavior and the Peter Principle.

(B) After the success of Google, some Silicon Valley
venture partners concluded that for company founders
they wanted graduate school dropouts. After the
success of Facebook, they concluded they wanted
college dropouts. After the success of Tumblr, they
concluded that they wanted founders who never went
to college, and we have to suspect that really they
wanted high school dropouts. They are also big on
recent immigrants who, necessarily, don't have a
Ph.D. degree from a US research university.

Getting a Ph.D. Below I give some advice on getting
a Ph.D. in 12 parts.

Qualifications: I hold a Ph.D. in Engineering from
a world famous US research university where my
research was on some applied math. I've been a
college professor teaching applied math and
computing, and I've worked in applied math and
computing for problems in business and US national
security. I've published peer-reviewed original
research in applied math and computer science.
Currently I'm a founder of a startup where the
crucial, core 'secret sauce' is some applied math I
created.

(1) Research. In any of the better US research
universities, very likely the main issue for getting
a Ph.D. is your research. In simple terms, do some
good research and find that your path is pleasant.
Struggle with research and find your life not so
good down to much worse.

So below I will give some ideas that can help you do
sufficiently good research.

(2) Criteria. The main criteria for research is
work that is "new, correct, and significant". Below
I will give some ideas that can help you achieve
each of these three criteria.

(3) Engineering. In the STEM fields, I'd
concentrate on engineering. Of course the 'M' in
STEM is for mathematics, so there I'd concentrate on
some version of applied mathematics, e.g.,
'mathematical sciences', hopefully in a school of
engineering where your research can be some
mathematics for a practical problem. For just why
should concentrate on engineering, see below.

(4) Mathematize. For how to do good research in the
STEM fields, my recommendation is to 'be wise,
mathematize'. That is, quite broadly the most
respected research, especially in the STEM fields,
is to find mathematical solutions. Advantages of
mathematization:

(A) If you present your mathematical solution as
theorems and proofs, then it can be fairly easy for
you to check that your work is correct and quite
difficult for anyone else to argue that your work is
not "correct".

(B) In fields of engineering, nearly everyone
struggles with math. So, if you have a good math
background, then you can have one heck of an
advantage.

(C) Applied math is one astoundingly powerful way to
get good solutions to practical problems. So, (I)
start with a practical problem. (II) Find what
mathematical assumptions are reasonable for that
problem and make a faithful conversion of the real
problem into a mathematical problem. (III) Using
the assumptions, find a solid, powerful mathematical
solution to the mathematical problem. (IV) Convert
the mathematical solution to a real solution, e.g.,
via software. (V) Write a paper on the work (and/or
start a business to deliver the results). So, in
moving logically from the real problem to the real
solution (as a paper and/or business), you have
taken a detour through some mathematics; this detour
can be a big advantage over slogging through just
intuitive or empirical techniques.

(5) Achieving the Three Criteria. There is an
advantage in being in engineering: You are likely
permitted to start with a practical problem. If you
start with a recent practical problem, then nearly
any solution you find can be called "new" if only
because your problem was new. Or, if you are
working on a problem in large server farms, how the
heck did von Neumann, Kolmogorov, Maxwell, or Newton
have already solved it? If the practical problem is
important and you make some solid, visible progress
on it, then your work can be called "significant".
If your solution is mostly mathematics, with
theorems and proofs, then it's 'correct' essentially
only from passing checks on the theorems and proofs.

It can help your solution be regarded as
'significant' if in some sense it is provably the
best possible, that is, 'optimal'. So, maybe your
solution is the least cost, least time, least mean
square error, least type II error, etc.