[This is actually a really long comment on Curt Monash's post but I think it's worth cross posting here.]
Seeing as I have been doing a lot of thinking about database opportunities lately I'll wade in on MarkLogic's as well. I can't really comment about the specific verticals that MarkLogic sells into or should sell into. However, I see 2 fundamental problems with MarkLogic's product positioning.
First problem; they backed the wrong horse by focusing exclusively on XML and XQuery. This has been toned down a lot but the die is cast. People who know about MarkLogic (not many) know of it as a 'really expensive XML database that you need if you have lots of XML and eXist-db is too slow for you'. They've put themselves into a niche within a niche, kind of like a talkative version of Ab Initio.
This problem is obvious if you compare them to the 'document oriented' NoSQLs such as CouchDB and MongoDB. Admittedly they were created long after MarkLogic but the NoSQLs offer far greater flexibility, talk about XML only as a problem to be dealt with and use a storage format that the market finds more appealing (JSON).
Second problem; 'Enterprise class' pricing is past its sell by date. What does MarkLogic actually cost? You won't find any pricing on the website. I presume that the answer is that old standby 'whatever you're looking to spend'. Again, the contrast with the new NoSQLs couldn't be more stark - they're all either pure open source or open core, e.g., free to start.
MarkLogic was essentially an accumulator bet: 1st bet - XML will flood the enterprise, 2nd bet - organisations will want to persist XML as XML, 3rd bet - an early, high quality XML product will move into an Oracle-like position.
The first bet was a win, XML certainly has flooded the enterprise. The second bet was a loss; XML has become almost a wire protocol rather than a persistence format. Rightly or not, very few organisations choose to persist significant volumes of data in XML. And the third bet was loss as well; the huge growth of open source and the open core model make it extremely unlikely that we'll see another Oracle in the data persistence market.
The new MarkLogic CEO needs to acknowledge that the founding premise of the company has failed and they must pivot the product to find a much larger addressable market. Their underlying technology is probably very good and could certainly be put to use in other ways (Curt gives some examples). I would be tempted to split the company in 2; leaving a small company to continue selling and supporting MarkLogic at maximum margins (making them an acquisition target) and a new company to build a new product in start-up mode on the foundations of the existing tech.