NoSQL vs. SQL when scalability is irrelevant
Yes, sometimes RDBMS are not the best solution, although there are ways to accomodate user defined fields (see XML Datatype, EAV design pattern, or just have spare generic columns) sometimes a schema free database is a good choice.
However, you need to nail down your requirements before choosing to go with a document database, as you will loose a lot of the power you may be used to with the relational model
eg...
If you would otherwise have multiple tables in your RDBMS database, you will need to research the features MongoDB affords you to accomodate these needs.
If you will need to query the data in specific ways, again you need to research what MongoDB offers you.
I wouldnt think of NoSQL as replacement for RDBMS, rather a slightly different tool that brings its own sets of advantages and disadvantages making it more suitable for some projects than others.
(Both databases may be used in some circumstances. Also if you decide to go down the route of possibly using MongoDB, once you have researched the websites out there and have more specific questions, you can visit Freenode IRC #mongodb channel)
I don't think you should choose NoSQL datastore for its schema free design. Schema free design always existed in RDBMS via XML and some databases have good XML support. It is a lot easier to deal with a database than a NoSQL datastore. Scalability and big data should be the primary drivers to choose a NoSQL datastore otherwise the tradeoff of ACID and SQL is a lot to switch to NoSQL.
There are a lot of other conditions that I've been hearing about with non-relational systems vs relational. I prefer this terminology over sql/no-sql as I personally think it describes the differences better, and several of the "no-sql" servers have sql add-ons, so anyway.... what sort of concurrency pattern or tranaction isolation is required in your system. One of the purported differences between rel and non-rel dbs is the "consistent-always", "consistent-mostly" or "consistent-eventually". Relation dbs by default usually fall into the "consistent-mostly" category and with some work, and a whole lot of locking and race conditions, ;) can be "consistent-always" so everyone is always looking at the most correct representation of a given piece of data. Most of what I've read/heard about non-rel dbs is that they are mainly "consistent-eventually". By this it means that there may be many instances of our data floating around, so user "A" may see that we have 92 widgets in inventory, whereas user "B" may see 79, and they may not get reconciled until someone actually goes to pull stuff from the warehouse. Another issue is mutability of data, how often does it need to be updated? The particular non-rel db's I've been exposed to have more overhead for updates, some of them having to regenerate the entire dataset to incorporate any updates.
Now mind, I think non-rel/nosql are great tools if they really match your use case. I've got several I'm looking into now for projects I've got. But you've got to look at all the trade offs when making the decision, otherwise it just turns into more resume driven development.