Android - Running a background task every 15 minutes, even when application is not running

You have have detemined the amount of time (interval) to execute a snippet of code, its better to use AlarmManager because its more energy effient. If your app needs to listen to some sort of a event , then Service is what you need.

public static void registerAlarm(Context context) {
    Intent i = new Intent(context, YOURBROADCASTRECIEVER.class);

    PendingIntent sender = PendingIntent.getBroadcast(context,REQUEST_CODE, i, 0);

    // We want the alarm to go off 3 seconds from now.
    long firstTime = SystemClock.elapsedRealtime();
    firstTime += 3 * 1000;//start 3 seconds after first register.

    // Schedule the alarm!
    AlarmManager am = (AlarmManager) context
            .getSystemService(ALARM_SERVICE);
    am.setRepeating(AlarmManager.ELAPSED_REALTIME_WAKEUP, firstTime,
            600000, sender);//10min interval

}

Alarm Manager (system service) vs Remote Service with inner alarm implementation (separate process)?

Alarm Manager is your choice, because it already has what you need, you just have to set alarm intervals