You should do this. Other answers seem outdated.
NotificationCompat.Builder mBuilder =
(NotificationCompat.Builder) new NotificationCompat.Builder(context)
.setSmallIcon(R.drawable.some_small_icon)
.setContentTitle("Title")
.setContentText("This is a test notification with MAX priority")
.setPriority(Notification.PRIORITY_MAX);
setPriority(Notification.PRIORITY_MAX) is important. It can also be replaced with any of the following as per requirement.
Different Priority Levels Info:
PRIORITY_MAX --
Use for critical and urgent notifications that alert the user to a condition that is time-critical or needs to be resolved before they can continue with a particular task.
PRIORITY_HIGH --
Use primarily for important communication, such as message or chat events with content that is particularly interesting for the user. High-priority notifications trigger the heads-up notification display.
PRIORITY_DEFAULT --
Use for all notifications that don't fall into any of the other priorities described here.
PRIORITY_LOW --
Use for notifications that you want the user to be informed about, but that are less urgent. Low-priority notifications tend to show up at the bottom of the list, which makes them a good choice for things like public or undirected social updates: The user has asked to be notified about them, but these notifications should never take precedence over urgent or direct communication.
PRIORITY_MIN --
Use for contextual or background information such as weather information or contextual location information. Minimum-priority notifications do not appear in the status bar. The user discovers them on expanding the notification shade.
For more details check the following link:
http://developer.android.com/design/patterns/notifications.html#correctly_set_and_manage_notification_priority