Most Android and iPhone apps I have seen use an initial screen or dialog box to ask for credentials. I think it is cumbersome for the user to have to re-enter their name/password often, so storing that info makes sense from a usability perspective.
The advice from the (Android dev guide) is:
In general, we recommend minimizing the frequency of asking for user
credentials — to make phishing attacks more conspicuous, and less
likely to be successful. Instead use an authorization token and
Where possible, username and password should not be stored on the
device. Instead, perform initial authentication using the username and
password supplied by the user, and then use a short-lived,
service-specific authorization token.
Using the AccountManger is the best option for storing credentials. The SampleSyncAdapter provides an example of how to use it.
If this is not an option to you for some reason, you can fall back to persisting credentials using the Preferences mechanism. Other applications won’t be able to access your preferences, so the user’s information is not easily exposed.
You should use the Android AccountManager. It’s purpose-built for this scenario. It’s a little bit cumbersome but one of the things it does is invalidate the local credentials if the SIM card changes, so if somebody swipes your phone and throws a new SIM in it, your credentials won’t be compromised.
This also gives the user a quick and easy way to access (and potentially delete) the stored credentials for any account they have on the device, all from one place.
SampleSyncAdapter (like @Miguel mentioned) is an example that makes use of stored account credentials.
I think the best way to secure your credential is to first think of storing the Password with encryption in the account.db file which couldn’t be easily available in non rooted devices and in case of rooted device the hacker must need the key to decrypt it.
Other option is do all your authentication like the way Gmail is doing. after the first authentication with the Gmail server . you got the Auth Token that would be use in case of your password . that token would be store in plain text.this token could be false in case you change the password from Server.
the last option I’d recommend you to enable 2-Factor Authentication & create Device Specific Password for your device. After losing device, all you need is to disable that device.