One of my targets was the entity system used to describe a scene in video games. Conventionally this involves an OO hierarchy of some kind, either compositional or inheritance based. The problem is that you don't know up front all of the sorts of properties an entity will need and what algorithms it will work with; the integration of the various subsystems acting upon an entity is a high-maintenance area and tends to involve messy boilerplate data tracking. I pursued the problem further, and came up with a way to move the integration process out of the subsystems code.
This was done by creating a customized set of collections(array, key-value, bag) that associate their data against an entity structure, can handle multiple instances of data associated against the same entity, can efficiently access data of a specific entity, and can remove all of the data related to that entity upon a despawn request. Once these constraints are satisfied, the only thing each subsystem has to do is work with those collections.
Also of interest, and still in progress, is an implementation of J. Paul Morrison's "Flow Based Programming" concepts to control overall program structure. I was looking around at ways to minimize coupling, and this particular method added a degree of structure and contractual behavior.
The first thing that happened after taking on this concept was to work through the ramifications for interactive programs: I had to start with a big data structure containing all the state, and then split it out and merge it together to attain synchronized behaviors. This in turn motivated the entity system idea. It's a very spatial model, so I am now doing some work on a graphical tool.
NoFlo is an example of a more finished FBP implementation than mine: http://noflojs.org/
I have some other ideas too, but they're in a very early stage so there's little to say. Having prior experience in the domain is a huge help, and I wouldn't be taking this approach to conquer arbitrary new problems. I'd try to make at least one mess first ;)