We've been working on a systematic framework to guide choice of appropriate representation technique for different purposes. Although some aspects of this issue have already been covered by the field of knowledge representation within Artificial Intelligence, and by Tufte's work on graphical representations, there's a need for a framework that's broader than the one in knowledge representation, and more theoretically grounded than the one in Tufte's work.
The diagram below shows an example from our work. It takes two concepts that are usually viewed as opposites (liking and disliking) and treats them as two separate dimensions, both running from low to high.


Representation resources:
This article gives an overview of our approach as a whole.
Beyond the 80:20 principle: This article describes our work on going beyond the 80:20 (aka Pareto) principle.
Binary yes/no categorisation is usually simplistic and misleading; this article discusses richer categorisations.
Card sorts are useful not only for eliciting information, but also for showing the mental categories that people use.

Connectionism is a way of representing knowledge that's very different from nested boxes or hierarchies.
Facet theory makes it possible to use more than one categorisation for the same topic at the same time.
Fuzzy boundaries between categories are common; this article describes ways of representing them visually.
Gender categorisation is complex; this article shows ways of representing set theory via richer visualisations.
Graph theory is invaluable for representing networks, and chains of connections. This article is a brief introduction.
Representing lesson structure graphically: This article shows how a lesson can be planned systematically with diagrams. 
Schema theory and script theory involve people's mental templates for concepts and activities.
Showing the weight of evidence for and against an argument can be done in various ways, as described in this article.
Timelines are a useful notation for recording sequences of activities.
Trees and nets are concepts from graph theory that are invaluable for expressing concepts more rigorously.