In this blog post, MongoDB gives a high level overview on how document databases are particularly suited to ecommerce (as well as analytics). There are a few people who are using MongoDB for ecommerce, and I think that this is one area where document databases will perform well.
There is yet to be an open source ecommerce application which uses a document database (to my knowledge). Perhaps the start could be for Mongo, Apache, or some other open source project to release a the document equivalent to a ‘reference schema’ for an ecommerce application.
There is some work being done on the Vespolina project (which uses MongoDB and Symfony2) here:
It would be great to hear from people about other efforts!