Document stores shine in that case. Depending on the exact case something like postgres's HSTORE, couchdb, couchbase, mongodb or similar would work. They're all capable of storing arbitrary json docs under a given key and efficiently retrieve it. Partial indexing is possible as well.
I don't think that amount of information is really suitable for a database? It may be larger in some cases too, so there's not guarantees I can even make about size.