WP-Push combines an iOS/Android app with a WordPress plugin that lets you send notifications for various events from your WordPress install to your smart phone.

According to the plugin description,

Currently supported notifications new users, comments, pingback/trackbacks, user specific password reset notifications, and notifying authors of comments on their posts if they add their user key to their profile.

The system also supports extensions. There are currently a small number of extensions available on the WP-Push website, such as one that could be used to alert a user to new topics created in a BBPress install (for example, if you had a forum set up specifically for paying customers who need support).