I'd like to see arbitrary graph based systems where there's no restriction on the relationships you can create - although doing so takes more work than dumping things into hierarchies. Tag based systems are useful for making the transition to graphs, but they're really just "patching" graph-like semantics onto trees - as are things like symbolic links in file systems.
Relationships are largely arbitrary, and what is meaningful to one person may not be to another. In order to have an effective system, I think it would need both a distributed and local component, such that there is this large, distributed graph of knowledge of relationships, which you can download and cache parts of selectively - and which you can add your own relationships to, and chose which of those you wish to share. By collectively sharing relationship, we can form consensus models which converge around specific kinds of ontologies - which could be used to optimise storage and querying for local caches of such boundaries.
My biggest gripe is perhaps this idea of bottom-up-schema creation, in which we try to conjure up a model of relationships which may work based on our limited knowledge of the models we want to express. Instead, the graph based approach gives us a top-down-approach, where all the relationships are visible, but where we focus on specific relationships to build an ontology, then optimise our problem around it.
Filesystems in the traditional sense are far too limiting in that they already push a bottom-up schema on you - that of files, and much of the data you want to organize isn't files anyway. The filesystem is useful though, and necessary to remain compatible with existing systems - but I think it should take the top-down approach, where for example, you'd have some FUSE module which accesses part of a larger graph database, and only cares about the file specific relationships or ontologies.
I'm no expert on graph theory, and I've only played around with the ideas a bit using existing graph databases (Titan, Orient, rel etc) and querying languages like Gremlin and Datalog. I also have a few dozen databases I've made with Postgres in order to map the relations I care about with refeences to external information sources (e.g musicbrainz) - some of which are not "open" in the sense that you'd want them in a distributed system, because they require sign-ups to central services in order to manipulate them.
I've also looked at various attempts to build systems like this, but the majority are proprietary systems, or centralized in some way or another, and I've not discovered a sane way to locally cache the data I want without taking whole copies of the databases.
At present there's just too much for me to learn and research, and not the time or motivation to do it - partly because I feel it would need to be a collaborative, free software project, as the profit motive is largely incompatible with the need for a distributed system - and I'm too focused on making a living right now.