As another poster pointed out, this is a false dichotomy. We're emerging from a technology monoculture of "every DBMS must be SQL" to "it's possible, even viable to design, implement and use a DBMS that does not implement SQL". Anyone advocating a mass exodus from SQL-land is a fool. Props to the NoSQL guys for opening our eyes to fresh ideas.
There's no need to stick with any single DBMS platform for 100% of your organization, unless you're so small that you have but one server total, and then I suspect this debate is largely irrelevant to you anyhow.
We're not Google, but we have some of the same problems Google faced with scaling up our applications for the Internet. We do use MySQL, having some 35+ instances of it. Our application processes in excess of 1000 transactions each second, and we know it'll be difficult to scale to tens of thousands of transactions per second without some fundamental changes. Today we survive by imposing limitations on developers writing OLTP applications--things like "all row operations must search by primary key" and "no table scans, ad-hoc queries or file sorts". The access language is still SQL, but increasingly we don't *need* SQL for OLTP transactions. We could plug in something today that is equivalent and far simpler.
What we're lacking in SQL-land is a good way to host DBMS applications on distributed infrastructure, e.g. in the cloud. There are clustered databases available, but these often require fast/short interconnects, may have difficulty scaling above bandwidth limits on a local network or SAN, and can be frustratingly fragile to use in the "real world". Not to mention expensive. This is due to the consistency model imposed on such systems, i.e. the "AC" in ACID.
Data sharding is a popular way to exceed the limits of SQL, but once you introduce sharding you're treading on "NoSQL" waters already. You can't retrofit sharding onto an application that isn't aware of it, not very successfully, in my experience. So developers need to become acutely aware of the storage tier and design for it, meaning they've already lost the perfect abstraction of SQL.
I'm keenly interested in emerging products like the Cassandra database, and while I have no intent of ever abandoning SQL (and probably even MySQL) in our organization, we're absolutely going to take "NoSQL" for a spin to see what it delivers in terms of cost, complexity, relability and performance.