The benefits of a non-relational database (such as a key-value pair storage) are evident when used in large scale datasets (google, facebook, linkedin). How do you think small to medium sized applications can benefit from using non-relational databases?
IBM Mainframes have had "non-relational" databases since the 60s (hierarchial databases such as IMS + variants). These databases are still in use because they are extremely fast and handle huge scale well.
The point of relational databases was to provide a regular, relatively abstract method for storing and retrieving data in which the tuning can be done relatively independently of the data model (not true for IMS). They were designed rather in reaction to the inability to reorganize hiearchical databases easily. The upside is nice organization; the downside is medium, not high performance.
Google provides scalable storage and MapReduce to handle scale. It isn't relational.
There was a huge push early in the last decade to store data in XML, in essentially hiearchical form because XML is implicitly hierarchical. That was a huge mistake IMHO, because it repeated the inconvenience of heirarchical databases, but had none of the performance. I'm not very surprised this movement seems to have pretty much died.
Most of the practical push to non-relational seems to me to be towards performance and scale. I don't see how this helps "small" applications much.
People have proposed, but not done a lot of practical data management using knowledge-based schemes. Doug Lenat's CYC comes to mind here. The ability of the database to help an application draw non-obvious conclusions strikes me a very interesting for "small" applications that are trying be "smart". But there aren't a lot of these yet.