I think for transactional systems , ACID will be core. But for OLAP kind of systems , transaction , integrity will not so important.

You might want to look at CAP theorem

http://en.wikipedia.org/wiki/CAP_theorem

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I will agree with Saptarsi Goswami.

The NoSQL databases are having and will have their own niche in the database world. The main focus of the NoSQL remain the same: (a) rapid solution creation (when the NoSQL is faster for utilization); (b) absence of the strict data integrity and tolerance to the some data lost, (c) the absence of the strict schema (or schema ""on the fly"), etc.

I think that in the near future they will have to deal with some sort of consistency issues specially for critical applications. Most business databases (transactional) works with strong consistency but lack the high performance of NoSQL databases. Trading of performance with consistency is not a solution. some attempts have been done to add transactions to NoSQL databases such as http://www.vldb.org/pvldb/vol6/p1434-dey.pdf in VLDB2013. I believe it will come to a point in the future that there will be transactions (consistency) without losing the high performance of NoSQL databases.

NoSQL Systems mainly focus on BASE theorem. As, consistency is compromised to maintain scalability. NoSQL systems are come into database world, because of big data storage.

You might be interested on this video of Dave Rosenthal from FoundationDB: NoSQL and ACID: http://youtu.be/1KsZKRcgmuU