How to get the Android device's primary e-mail address

There are several ways to do this, shown below.

As a friendly warning, be careful and up-front to the user when dealing with account, profile, and contact data. If you misuse a user's email address or other personal information, bad things can happen.

Method A: Use AccountManager (API level 5+)

You can use AccountManager.getAccounts or AccountManager.getAccountsByType to get a list of all account names on the device. Fortunately, for certain account types (including com.google), the account names are email addresses. Example snippet below.

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;
        ...
    }
}

Note that this requires the GET_ACCOUNTS permission:

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

More on using AccountManager can be found at the Contact Manager sample code in the SDK.

Method B: Use ContactsContract.Profile (API level 14+)

As of Android 4.0 (Ice Cream Sandwich), you can get the user's email addresses by accessing their profile. Accessing the user profile is a bit heavyweight as it requires two permissions (more on that below), but email addresses are fairly sensitive pieces of data, so this is the price of admission.

Below is a full example that uses a CursorLoader to retrieve profile data rows containing email addresses.

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;
    }
}

This requires both the READ_PROFILE and READ_CONTACTS permissions:

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

This could be useful to others:

Using AccountPicker to get user's email address without any global permissions, and allowing the user to be aware and authorize or cancel the process.

I would use Android's AccountPicker, introduced in ICS.

Intent googlePicker = AccountPicker.newChooseAccountIntent(null, null, new String[]{GoogleAuthUtil.GOOGLE_ACCOUNT_TYPE}, true, null, null, null, null);
startActivityForResult(googlePicker, REQUEST_CODE);

And then wait for the result:

protected void onActivityResult(final int requestCode, final int resultCode,
                                final Intent data) {
    if (requestCode == REQUEST_CODE && resultCode == RESULT_OK) {
        String accountName = data.getStringExtra(AccountManager.KEY_ACCOUNT_NAME);
    }
}