Pattern emailPattern = Patterns.EMAIL_ADDRESS; // API level 8+
Account[] accounts = AccountManager.get(context).getAccounts();
for (Account account : accounts) {
    if (emailPattern.matcher(account.name).matches()) {
        String possibleEmail = account.name;
        ...
    }
}

<uses-permission android:name="android.permission.GET_ACCOUNTS" />

public class ExampleActivity extends Activity implements LoaderManager.LoaderCallbacks<Cursor> {
    public void onCreate(Bundle savedInstanceState) {
        super.onCreate(savedInstanceState);
        setContentView(R.layout.activity_main);
        getLoaderManager().initLoader(0, null, this);
    }
 
    @Override
    public Loader<Cursor> onCreateLoader(int id, Bundle arguments) {
        return new CursorLoader(this,
                // Retrieve data rows for the device user's 'profile' contact.
                Uri.withAppendedPath(
                        ContactsContract.Profile.CONTENT_URI,
                        ContactsContract.Contacts.Data.CONTENT_DIRECTORY),
                ProfileQuery.PROJECTION,
 
                // Select only email addresses.
                ContactsContract.Contacts.Data.MIMETYPE + " = ?",
                new String[]{ContactsContract.CommonDataKinds.Email.CONTENT_ITEM_TYPE},
 
                // Show primary email addresses first. Note that there won't be
                // a primary email address if the user hasn't specified one.
                ContactsContract.Contacts.Data.IS_PRIMARY + " DESC");
    }
 
    @Override
    public void onLoadFinished(Loader<Cursor> cursorLoader, Cursor cursor) {
        List<String> emails = new ArrayList<String>();
        cursor.moveToFirst();
        while (!cursor.isAfterLast()) {
            emails.add(cursor.getString(ProfileQuery.ADDRESS));
            // Potentially filter on ProfileQuery.IS_PRIMARY
            cursor.moveToNext();
        }
 
        ...
    }
 
    @Override
    public void onLoaderReset(Loader<Cursor> cursorLoader) {
    }
 
    private interface ProfileQuery {
        String[] PROJECTION = {
                ContactsContract.CommonDataKinds.Email.ADDRESS,
                ContactsContract.CommonDataKinds.Email.IS_PRIMARY,
        };
 
        int ADDRESS = 0;
        int IS_PRIMARY = 1;
    }
}

<uses-permission android:name="android.permission.READ_PROFILE" />
<uses-permission android:name="android.permission.READ_CONTACTS" />