I have been addicted to Apple’s Push Notification Service ever since I bought Prowl . There are endless possibilities on what you can do with Push Notifications.
Apple’s Push Notification Announcement
The Apple Push Notification Service is a mobile service created by Apple Inc. that was released with iPhone OS 3.0 on the 17th June 2009. It uses push technology through a constantly-open IP connection to forward notifications from the servers of third party applications to the iPhone or iPod Touch; such notifications may include badges, sounds or custom text alerts.
Apple first announced the service on 9 June 2008 with a slated release for that September; however, as stated by Scott Forstall at the iPhone 3.0 preview event on 17th March 2009, the rollout was rolled back in September after a decision to restructure the APNS for scalability purposes due to the allegedly “overwhelming” response to the announcement of the APNS. At both events, Forstall stated that push notifications were a better means to maintain battery life than background processes (which are used for pull technology) as far as receiving notifications are concerned.
APNS is using XMPP/Jabber, particularly the PubSub extension.
Wikipedia: Apple Push Notification Service 
For reminders, there is NotifyMe  to notify you of things to do
For bills payment, there is BillMinder  to ensure you will not miss your bill payment.
The list is not comprehensive, there are much more iPhone apps that make use of Push Notification. Mashable also has a post on it, 14 iPhone Apps With Push Notification for Productivity .
For web developers like me, I love Prowl , because there is an API  for you to use and ready made classes for
Perl, PHP, Python, Ruby, Java and Lasso. Do note that the IP addresses are limited to 1000 API calls per hour which is better than Twitter’s 150 API calls.
With Prowl, you can customized your own Push Notifications. For me, I have my this web server’s cron setup to check my Twitter account for new mentions and direct messages every 5 minutes and if there are any, it will notify Prowl using the API and Prowl will sent a Push Notification to my iPhone.
If anybody post a comment in this blog, Prowl will also notify me as I have hooked it into WordPress. Next I am thinking of using my backup server’s cron to ping this site every 1 hour, and if there is any downtime, it will also sent a Push Notification to my iPhone. As mentioned earlier, there are endless possibilities on what you can do with Push Notifications using Prowl + Webserver + Cron.