What applications/IDEs are out there to develop BASE database systems from?
BASE systems (Basically Available, Soft state, Eventually consistent) are an alternative to RDBMS, that work well with simple data models holding vast volumes of data. Google's BigTable, Dojo's Persevere, Amazon's Dynamo, Facebook's Cassandra are some examples.
Seems like you are looking into the recently popular NoSQL moniker for "databases". Which also includes MongoDB, Voldemort (must not be named), Hbase, Tokyo Cabinet, CouchDB. There are a lot of them. Not sure what your question is?
Each one has it's own advantages, implementation difficulty, and performance differences. Although they are all designed to scale. There are some good articles on highscalability.com. http://highscalability.com/blog/tag/nosql
Then there are the systems that are designed to enhance and scale searching from traditional databases (i.e. MySQL). For example, Solr based on Lucene. That's more geared towards full text searching. That falls in the "eventually consistancy" since it syncs with the database periodically.