MongoDB is most popular NoSQL database that is used by many of the fortune 500 companies and is very relaible for storing large amount of data.
Here we are listing the services that provides free hosting for your mongodb databases.
Mlab is most popular mongoDB hosting service. It provide 0.5GB of data storage for free with paid plans starting from 15$/GB.
MongoDB.com is the main developer behind the mongoDB database. They provide 512 MB database for free. They call the free service sandbox mode.