Well a major con would be the mismatch between Java and a DB. That's a big headache if you don't need it. It would also be a lot slower for really simple access. On the other hand, the benefits would be transactions and persistence to the file system in case of a crash. Also, depending on your needs, it allows for querying in a way that might be difficult to do with a regular Java data structure.
For something in between, I would take a look at Neo4j. It is a pure Java graph database. This means that it is easily embeddable, handles concurrency and transactions, scales well, and does not have all of the mismatch problems that relational DBs have.
Updated If your data structure is simple enough - a map of lists, map of maps, something like that, you can probably get away with either the concurrent collections in the JDK or Google Collections, but much beyond that, and you will likely find yourself recreating an in memory database. And if your query constraints are even remotely difficult, you're going to have to implement all of those facilities yourself. And then you'll have to make sure that they work concurrently etc. If this requires any serious complexity or scale(large datasets), I would definitely not roll your own unless you really want to commit to it.
If you do decided to go with an embedded DB there are quite a few choices. You might want to start by considering whether or not you want to go the SQL or the NoSQL route. Unless you see real benefits to go SQL, I think it would also greatly add to the complexity of your app. Hibernate is probably your easiest route with the least actual SQL, but its still kind of a headache. I've done it with Derby without serious issues, but it's still not straightforward. You could try db4o which is an object database that can be embedded and doesn't require mapping. This is a good overview. Like I had said before, if it were me if I would likely try Neo4j, but that could just be me wanting to play with new and shiny things ;) I just see it as being a very transparent library that makes sense. Hibernate/SQL and db4o just seems like too much hand waving to feel lightweight.