There's growing dissatisfaction with SQL on a number of fronts, but it seems hard to tell if this represents an actual movement or just a loose coalition of groups with slightly aligned interests.
The most prominent members of the 'NoSQL' movement are proponents of new data management schemas such as Hadoop and MapReduce, the latter being a new approach to data management pioneered by Google. Vendors that have embraced these approaches include Aster Data and ParAccel.
A less prominent faction of the 'NoSQL' movement comes in the form of companies such as Mark Logic, which makes an XML database that supports the Xquery language for accessing unstructured content in preference to a derivative of SQL.
While these factions represent the major technology elements of the backing the 'NoSQL' initiative, there are other IT folks lending their support because of their frustrations with database pricing, while others such as Terracotta simply want to reduce the database to a commodity by relying more on memcachedb approaches.
By leveraging the popularity of Google and other famous Web 2.0 companies that have eschewed the SQL database, the 'NoSQL' effort is now fashionable than ever.
Every faction in the 'NoSQL' movement has some legitimate issues, but as Mark Logic CEO Dave Kellogg points out the challenge with all movements is that they can become reactionary. There will probably always be a need for a SQL database. But that said, a SQL database does not need to be the center of the universe for all data. There are instances where the sheer volume of data or the very structure of the data makes another option more viable.
The real challenge will be getting existing database administrators to realize that.