Visio is the most conspicuous example of a program that I found useful on Windows for which I have not identified a Mac-compatible replacement.
Visio's primary function is as a flowchart diagramming tool. It allows the user to construct complex information flows with smart objects and interconnect graphics that snap and bend as the user moves things around on the page. It's morphed over the years to support other diagram and information flow views like IT diagrams and UI mockups.
What's out there that can replace Visio on the Mac?