I think the answer is yes. The reason is that traditionally relational datastores have ended up as being the dumping ground for data. Everything has ended up there and with the advent of new data storage technology there is a chance to rummage around the various piles of data and ask whether things are in the right home or not.
One thing I’ve been doing a lot recently is data-driving HTML Form components. That’s a lot easier when you are just reading the data out of documents and lists rather than out of tables. The first advantage is that you don’t have to size your option text for example. Variable text labels? No problem. The second is that you can move away from numeric values to having text-based slug keys or even use existing conventions like ISO language short codes.
You don’t have to use numbers with relational data of course but it tends to happen due to leaky ORM solutions that are orientated around the Long Primary Key.
Another area where you can probably take advantage of a NoSql store is in the small bits of text that occurs around your site but which should be maintained by business owners rather than the front-end team. Thing of those straplines, boxed text and success stories. Maybe they are stored in CLOBs somewhere in the database perhaps in a table called something cryptic like user_text. Let’s liberate that data into a key-store!
I find myself using a lot of Textile and Markdown text in my sites and it is an almost trivial exercise to process and display it from a NoSql database. I would encourage you to give it a go, it’s low risk but it should illustrate some of the benefits of the new stores and suggest the kinds of other problems you have in your application that some NoSql could solve.