Parse - Build applications faster with object and file storage, user authentication, push notifications, dashboard and more out of the box.
AWS Mobile Services - Storage, Analytics, Push Notif. & SMS Delivery SDKs
MongoDB Stitch - The serverless platform from MongoDB
Azure Mobile Apps - Build engaging cross-platform and native apps for iOS, Android, Windows or Mac with Azure's Mobile App Service.
Apache UserGrid - Usergrid is an open-source BaaS enabling developers to rapidly build web and/or mobile applications.