I've got an app running on AWS. How do I set up Amazon CloudWatch to notify me when the EC2 instance fails or is no longer responsive?
I went through the CloudWatch screens, and it appears that you can monitor certain statistics, like CPU or disk utilization, but I didn't see a way to monitor an event like "the instance got an http request and took more than X seconds to respond."
CloudWatch monitoring is just like you have discovered. You will be able to infer that one of your instances is frozen by taking a look at the metrics, but CloudWatch won't e.g. send you an email when your app is down or too slow, for example.
If you are looking for some sort of notification when your app or instance is down, I suggest you to use a monitoring service. Pingdom is a good option. You can also set up a new instance on AWS and install a monitoring tool, like Nagios, which would be my preferred option.
Good practices that are always worth, in the long road: using load balancing (Amazon ELB), more than one instance running your app, Autoscaling (when an instance is down, Amazon will automatically start a new one and maintain your SLA), and custom monitoring.
My team has used a custom monitoring script for a long time, and we always knew of failures as soon as they occurred. Basically, if we had two nodes running our app, node 1 sent HTTP requests to node 2 and node 2 to 1. If any request took more than expected, or returned an unexpected HTTP status or response body, the script sent an email to the system admins. Nowadays, we rely on more robust approaches, like Nagios, which can even monitor operating system stuff (threads, etc), application servers (connection pools health, etc) and so on. It's worth every cent invested in setting it up.