Notifications are great for... well, when you have things that you'd like to notify your users about.
For one example that is applicable to nearly every app, albeit indirectly, it can be used to notify users when you have released a new app. I don't mean an update to that app, but if you were to release a brand new app under the same name, you can use your existing user base to promote this new app.
If the face of your development efforts (i.e., "(Your Name) Studios") keeps a blog of news and going-ons, you could use push notifications to keep your user base up to date and interested in what you're working on.
Push notifications are indeed a very cool thing with a lot of applications if you think hard enough.