Pushover
Pushover is a service to get push notifications on Android, iOS, and desktop systems.
Pushover offers a simple API.
IndieWeb Examples
David Shanske uses Pushover to receive webmention and IRC notifications
Barry Frost uses Pushover to notify him of webmentions (including unsuccessful webmention attempts)
Kyle Mahan added support for sending Pushover notifcations when webmentions are received in Red Wind.
Costs
Pushover offers a free five-day trial. After that, it costs a one-time license fee, currently $4.99 to purchase the app for your platform. Once the app is purchased for the platform, it can be used on unlimited devices.
Each application registered to Pushover can send 7500 messages per month for free, which is sufficient for most personal uses.
For high-volume applications that need to send more than 7,500 messages per month, additional capacity can be purchased (currently 10,000 for $50.00 USD, 25,000 for $115.00 USD, 50,000 for $225.00 USD). Once an application uses its free allowance, subsequent messages will start deducting from its purchased reserve until the first of the next month.