How can I delete a Facebook app that I developed?

The alternative to deleting the app is to place it in sandbox mode. This will preserve your application id and keys and save you time in the future.

Just click on Settings>Basic then set "Sandbox Mode" to Enabled.

UPDATE 9th June, 2016

• Navigate to facebook developer account

• Select the application to which you'd like to make changes to

• Navigate to Settings->Advanced on the left panel.

• In the bottom left of the screen you will find Delete App

Navigate to the developer application, select the application, and click the edit button:

Then, on the left side of the page, there is a link you can click to delete your application:

Go here.

Click on the 'Delete App'. Give your password. Done :)