I think that the ability to send programmatic in-app notifications using a Notifications API would be a great addition to HubSpot.
Use-Cases:
1. I have a swag system that sends swag packages to contact its connected to HubSpot using custom objects and it would be really nice if I could send a notification to the owner when a package is delivered.
2. When a HubSpot user hits the quota for contact prospecting, send a notification.