Example of a task that a NoSQL database can't handle (if any)

Question

I would like to test the NoSQL world. This is just curiosity, not an absolute need (yet). I have read a few things about the differences between SQL and NoSQL databases. I'm convinced about the potential advantages, but I'm a little worried about cases where NoSQL is not applicable. If I understand NoSQL databases essentially miss ACID properties.

Can someone give an example of some real world operation (for example an e-commerce site, or a scientific application, or...) that an ACID relational database can handle but where a NoSQL database could fail miserably, either systematically with some kind of race condition or because of a power outage, etc ?

The perfect example will be something where there can't be any workaround without modifying the database engine. Examples where a NoSQL database just performs poorly will eventually be another question, but here I would like to see when theoretically we just can't use such technology.

Maybe finding such an example is database specific. If this is the case, let's take MongoDB to represent the NoSQL world.

Edit: to clarify this question I don't want a debate about which kind of database is better for certain cases. I want to know if this technology can be an absolute dead-end in some cases because no matter how hard we try some kind of features that a SQL database provide cannot be implemented on top of nosql stores. Since there are many nosql stores available I can accept to pick an existing nosql store as a support but what interest me most is the minimum subset of features a store should provide to be able to implement higher level features (like can transactions be implemented with a store that don't provide X...).