Visualizing the DOM
All modern browsers have a tab in their dev tools that allows traversing the DOM tree.
Mozilla wrote a neat little tool called Tilt a few years ago that allowed developers to view a 3D layout of their pages based on the DOM.
It's important to note that what you see in these visualizations of the DOM is not quite literally the DOM, as Chris Coyier mentions in his own What is the DOM? post.
The DOM is a structured abstraction of a document.
Abstractions usually have trade-offs. In the case of the DOM as implemented today in modern web browsers, there is considerable debate going on. As we move into a web of apps instead of documents, the future of the DOM, how browsers utilize it to build their render tree, how libraries utilize it and how we build apps and UIs on top of it is in flux.
Stay tuned for upcoming trends and standards that change how web developers interact with the DOM and, subsequently, how sites and application UIs are build.
For some more history and more detail into how web browsers implement Plain Old DOM, dive into the following: