Is there a database out there that gives you the benefit of referential integrity and being able to use a SQL type language for querying, but also lets entities be loosely defin
Given the requirements you specify in your question, a graph database is probably the sort of thing you are looking for, but there are other options. As @Niels van der Rest said, the two constraints of "no a priori schema" and "referential integrity" are very hard to reconcile. You might be able to find a Topic-Map based database that might do so, but I'm not familiar with specific implementations so I couldn't say for sure.
If you decide you really can't do without referential integrity, I fear you probably are stuck with an RDBMS. There are some tricks you can use that might avoid some of the problems you anticipate, I cover a couple in https://stackoverflow.com/questions/3395606..., which might give you some ideas. Still, for this sort of data-model requiring dynamic, post-priori schema, with meta-schema elements, an RDBMS is always going to be awkward.
If you are willing to forgo referential integrity, then you still have three approaches to consider.
Map/Reduce - in two flavours: distributed record-oriented (think, MongoDB), and column-oriented (think, Cassandra). Scales really really well, but you won't have your SQL-like syntax; joins suck; and matching your architecture to your specific query types is critical. In your case your focus on the entities and their attributes, rather than the relationships between the entities themselves, so I would probably consider a distributed record-oriented store; but only if I expected to need to scale beyond a single node—they do scale really really well.
Document-store - technically in two flavours, but one of them is a distributed record-oriented map/reduce datastore discussed above. The other is an inverted-index (think, Lucene/Solr). Do NOT disregard the power of an inverted-index; they can resolve obscenely complex record predicates amazingly fast. What they can't do is handle well is queries that include correlation or large relational joins. Still, you will be amazed at the incredible flexibility, sufficiently complex record predicates gives you.
Graph-store - come in a few flavours the first is the large-scale, ad-hoc key-value store (think, DBM/TokyoTyrant); the second is the tuple-space (think, Neo4j); the third is the RDF database (think, Sesame/Mulgara). I have a soft-spot for RDF, having helped develop mulgara, so I am not the most objective commenter. Still, if your scalability constraints will permit you to use an RDF-store, I find the inferencing permitted by RDF's denotational semantics (rare amongst noSQL datastore options) invaluable.