Most of these offer similar services: cloud file & data storage, push notifications, and native iOS SDK libraries. Some also include user management, social features (enabling logins through Facebook and Twitter) and analytics.
Most include a free tier, with paid tiers for higher traffic.
- Google Mobile Backend Starter
- Dropbox has a Sync API for syncing files, and a Datastore API for database-like data storage.
- StackMob - data store, push notifications, geolocation, social, file storage/syncing with Amazon S3.