Having played around with NoSQL databases recently ( CouchDB ), I can't imagine they are the answer! Maybe my brain is too wired to think in terms of tables, but my god the experience sucked beyond simple document storage. If you are storing your data as a blob ( say a chunk of JSON ) that you grab, update then push back to the database, it works smashingly, but updating a single value within that document causes an entire new revision to be created. Now, storing files in a NoSQL database is an order of magnitude easier then a relational database, but actual data, not so much.
Well.. that's one example of a NoSQL database. Compare that to Redis (http://www.redis.io) which is used by Blizzard Entertainment, Stackoverflow, Github, Flickr, Craigslist.. we use Redis for custom news views on the frontpage as well as for real-time access to member data in the Top Members section (http://www.gamedev.net/sm/)
Blizzard uses an 8 node redis cluster for serving avatars in World of Warcraft. Redis is an in-memory data structure server with persistence capabilities.
Also with your situation games not necessarily save in realtime to disk.. with most it's sufficient to do periodic checkpoint saves.