Previously #include statements were a bit of a mess across the codebase.
This commit is the result of a pass by the IWYU (Include What You Use)
tool, which suggests headers to add or remove based on what is in the
file, and can also suggest forward-declaring classes instead of
including their headers, if they are only used as a pointer in a
particular file. Cleaning this up should in general speed up compile
times.

IWYU isn't perfect, it produces a number of false positives, so we don't
try to automate this process and we don't accept all of its
recommendations. We do add a script and configuration file to the tools/
directory so that IWYU can be every so often in the future.

We also clean up all the includes according to a consistent style, which
is now described clearly in the C++ style guide.