What programs/IDEs are available to build up BASE database systems from?

BASE systems (Essentially Available, Soft condition, Eventually consistent) are an alternative choice to RDBMS, that actually work well with simple data models holding huge volumes of information. Google's BigTable, Dojo's Persevere, Amazon's Dynamo, Facebook's Cassandra are a handful of good examples.

It appears as if you are considering the lately popular NoSQL moniker for "databases". That also includes MongoDB, Voldemort (mustn't be named), Hbase, Tokyo Cabinet, and CouchDB. You will find many of them. I don't know what your real question is?

They all have its very own advantages, implementation difficulty, and gratifaction variations. Although they all are made to scale. You will find good quality articles on highscalability.com, http://highscalability.com/blog/tag/nosql

Then you will find the systems that can enhance and scale searching from traditional databases (i.e. MySQL). For instance, Solr according to Lucene. That's more targeted towards full text searching. That falls within the "eventually consistency" because it synchronise using the database periodically.