I picture clusters of information as they move through the computer. Sometimes they look like ships or motorcycles. :-)
Usually, I don't visualize anything in particular. I use tools for visualization, but I prefer to think algebraically. If I work on a complicated system, programming to me feels like like moving through a landscape, with points of interest that I memorize or lay out spatially in a tool, and going through the motions like patching things together, flicking switches, plugging things in and out etc.
I have been pondering about this issue for a while. Maybe it is inevitable that successful systems turn into big balls of mud eventually once the "inflection" point has been reached and (slow) deterioration begins.
It is somewhat of a clichè but I think that (interactive) documentation and tooling can make a difference, but it is very difficult to design the process and the tooling to be as frictionless as possible. Tudor Girba and his team at feenk have been doing a lot of interesting work in that area that's worth a look [1, 2].
The software in question might be an entangled mess, a large part of it might be even inherent due to its requirements or technical constraints, but if that messy web can be readily augmented with background information and sign-posts I think the situation could be significantly improved.
On a related note, there has been a project at Xerox PARC called PIE (Personal Information Environment) [3] which has put forward the idea of organizing software and its artifacts (source code, various kinds of documentation) as a network. Although that particular concept has never been adopted in any major programming system as far as I know, I think that it has huge potential, especially if the software, as a network, can be collaboratively navigated and extended with additional information, where and when needed -- online.
Now that all does not change the fact that we are still dealing with a ball (or a web) of mud, but at least it is accessible and we might have a better chance to understand its evolution and the reasons that made it complicated in the first place.
Usually, I don't visualize anything in particular. I use tools for visualization, but I prefer to think algebraically. If I work on a complicated system, programming to me feels like like moving through a landscape, with points of interest that I memorize or lay out spatially in a tool, and going through the motions like patching things together, flicking switches, plugging things in and out etc.