After becoming frustrated with the half-dozen Profiles that all do the same thing (except for subtle differences here and there), I have started on cleaning up my org's permissions scheme.
My basic idea is to have as few Profiles as possible, and a separate Permission Set for each task a User may perform in their job. This allows the organization to change position responsibilities flexibly, reduces my maintenance burden, and documents not only who has access to a thing, but why they have it.
I'm now fully bought into cutting out Profiles altogether, but I recognize that the platform isn't. What is the full set of things that Profiles control that I can't alter in Permission Sets?