Yes, there are many such services which are coming up now which give you a cloud data-store without writing code on cloud.
Listing some:
- http://parse.com/ (A facebook company now). They have a good free usage plan to start with, and is very easy to use (I have tried personally)
- https://www.firebase.com/
- AWS DynamoDB. If you are familiar with AWS, this is a good option.
- Dropbox Datastore
All of them give client side SDK - for Android, iOS etc.