I have a large semantic store (Jena SDB in this case, 30 million quads). I'm looking for a software or a library (Java or C#) that allows me to visualize / visually explore the data in the store.
The answer will depend on the sort of visualization you want to do which in turn depends on the shape of the data.
There is not that much in the way of visual exploration tools specifically for RDF. There is IsaViz and RDF Gravity (both of which use Jena) but I doubt those would be able to cope with your scale out of the box. For Ontologies then there are a lot of plugins for Protege such as Jumbalya - see this survey of Ontology visualization approaches. Mike Bergman did a great survey of 26 tools for graph visualizations for a large ontology concluding that Cytoscape was the most robust and flexible option for that use. There is also the new Gephi platform which sounds pretty interesting but is not specific to RDF.
For basic graph libraries which you could use to build something yourself then libraries that get good mentions include JUNG, JGraph, GINY and TouchGraph (commercial).
For more chart-like visualizations then JFreeChart tends to top the list of recommendations, also see this survey.
For a richer range of visualization options then Prefuse is worth a look as is Processing (though that is more a programmable environment than a library).
If you can generate a DOT format file which I think Jena has a writer for you can use GraphViz's command line tools to generate static visualisations in various formats.
GraphViz is highly configurable and supports multiple layout algorithms and visualisations
JUNG is a very useful toolkit for working with and visualising graphs in java. JenaJung provides little glue to make Jena models work as (read only) JUNG graphs.
+1 Cytoscape; Cytoscape handles big graphs without a lot of pain.