What are my different options of persisting data entered in an iPhone application?
NSUserDefaults: Small amount of data
Web Service: iOS code triggers web service and saves the data into the database
Can I save the data into some database which is present locally on the iPhone? If yes how does the user backup the saved data?
You can use SQLite directly or via Core Data. You just keep the db file in Documents directory of your app’s filesystem sandbox and iTunes/iCloud will back it up automagically.
In iOS 5, you can even store Core Data changes to iCloud automatically on every change and sync it between apps.