I was wondering if its possible to use a json-based schema-free, document-based database like Mongodb or Couchdb on a symfony project like its used for ruby-on-rails websites? And if yes, how can it be done?
You might get some help from the MongoDB PHP Language Center. There are links to several PHP libraries for MongoDB, including a centralized logger for symfony applications.
AFAIK, the only framework to have integrated Mongo support as of yet is Vork http://www.Vork.us
I saw a post from someone who retrofitted Cake to use MongoDB, but they basically had ro rewire the whole model-engine.
Try building your project with the no-orm flag. There is little need to have an object relational database if you are not using a relational database. Just build classes for your data in PHP. These will function as your schema, which makes sense sense as a schema is not defined at the data layer.
You can also check out http://lithify.me/, the only full-stack PHP framework with fully-integrated support for MongoDB (and CouchDB).