There's been a bit of debate about NoSQL databases. The Association for Computing Machinery has a discussion of non-interest in NoSQL.
In sum, the folks who are not interested in NoSQL databases want to remain with SQL for two reasons: their business uses OLTP and SQL offers ACID (atomic, consistent, isolated, and durable) transactions, and SQL is a standard.
I have some thoughts on this notion of non-interest.
No one is asking people to abandon SQL databases. The NoSQL enthusiasts recognize that OLTP needs the ACID properties. Extremists may advocate the abandonment of SQL, but I disagree with that approach. If SQL is working for your current applications, keep using it.
But limiting your organization to SQL with the reasoning: "transactions are what we do, and that's all that we do" is a dangerous path. It prevents you from exploring new business opportunities. The logic is akin to sticking with telegrams and avoiding the voice telephone. (Telegrams are written records and therefore can be stored, they can be confirmed and therefore audited, and they are the standard... sound familiar?)
SQL as a standard offers little rationale for its use. The folks I talk to are committed to their database package (DB2, SQL Server, Oracle, Postgres, MySQL, etc.). They don't move applications from one to another. (Some folks have moved from MySQL to Postgres, but the numbers are few.) Selecting SQL as a standard has little value if you stick with a single database engine.
For me, the benefit of NoSQL databases is... no SQL! I find the SQL language hard to learn and harder to use. My experience with SQL databases has been consistently frustrating, even with open source packages like MySQL. My experience with proprietary, non-SQL databases, on the other hand, has been successful. The performance is better and the code is easier to write. (Easier, but still not easy.) No SQL databases appeal to me simply to get away from SQL.
My preferences aside, NoSQL databases are worthy of investigation. They have different strengths and allow for the construction of new types of applications. Insisting on SQL for every database application is just as extremist as insisting on the complete removal of SQL. Both can contribute to your application suite. Use them both to your advantage.