I think Ryan Bates "How I test" screencast is a great example. It's specific to rails but I've used this approach on web applications in a few different frameworks. http://railscasts.com/episodes/275-how-i-test?view=asciicast

Basically, test the heck out of your domain model layer, and then do full stack acceptance tests above that to simulate the user using the app. If it's a web app use something like Capybara, if its a terminal app or some other interface, simulate that appropriately with some other kind of integration test.