My opinion is that app settings (or web.config settings) are generally overused. It is usually reasonable for developers to expect that certain values in their code will change in the future. The temptation is to capture all these variables in the app settings. Doing so however, is a mistake.
The only values that belong in application settings are things that will change with the environment, i.e. TEST, STAGE, PRODUCTION.
Everything else, including the things we think (or even know) will change belong directly in source code. I've learned this rule only over time, and I think its reinforced by the YAGNI principle.
Explanation
Sometimes business requirements are delivered in such a way that they barely need translating into a model or domain or even into some syntax. They will usually be very short user stories, and not scored very highly. Examples include:
"As a patient I want a reminder 1 hour before my appointment."
"As a broker I want the message push interval to be 10 seconds."
"As a user I want the warning message to read: 'Are you sure you want to delete?'"
The important thing about these stories to notice is the precision they provide. Product owners like precision. They like to know exactly what their product will or won't do. Developers however, like abstraction. They like removing precision and extracting the general rules behind the process. Developers see a rule like '... a reminder 1 hour before my appointment' and take from it the underlying purpose of the story: 'something must happen at a certain time before something else happens'.
There are clearly a number of ways in which sending the reminder could be implemented, depending on the delivery mechanism or format that I won't discuss. But what is clear is that our Product Owner wants the reminder sent 1 hour prior to the appointment. Most developers would look at this requirement and expect it to change. The one certainty about any piece of software is that it will need to change.
The temptation therefore is that the 1 hour (or 60 minutes) should not be hard-coded - if the value is going to change, then lets keep it somewhere where it's easy to change like the app settings, right? Wrong.
There are two reasons for this: Unit Tests and Continuous Delivery.
Unit Tests
The user story in question is business value waiting to be delivered. We want to be absolutely sure that we are delivering that value. If we ship code that doesn't have a passing unit test titled "A_Reminder_Is_Sent_60_minutes_before_appointment" then we haven't succeeded. (Or perhaps closer resembling conceivable objects something like "Reminder_Delivery_Time_Is_60_minutes_before_appointment_time"). We should be sure that no other changes we might make in future will interfere with this piece of logic.
You might argue that we could write a test that reads this value out of our app settings. But then what you would have is an integration test. The reason we want to capture this behaviour in a unit test is to get the answer we want in the shortest feedback loop possible. Also, we don't want to have to maintain a duplicate app settings file in our unit test project.
Continuous Delivery
The practice of automated deployment is becoming more common. As Scott Hanselman says, "If You're Using XCOPY, You're Doing it Wrong. I would take this further and say that if you are still RDC'ing onto the live server to edit a config setting (like changing 60 minute reminders to 120 minute reminders) then you're also doing it wrong. This means the ONLY way to deploy new code (or changed code) is to use an automatic task, and never tamper with the live servers. In a lot of cases developers do not even have access to the live servers.
So now that our app settings file is no longer accessible, it is certainly not easier to change. If we want to change our reminders from 1 hour to 2 hours we have to do so locally, commit and deploy.
Not forgetting our unit test of course - if we made our change in code and ran our tests we should expect a failure. This is important. We have changed the rules of the system and should expect to have to update our unit test accordingly. The new rules are then captured and protect our logic against future unexpected changes.
Environments
So when are App Settings useful? The purpose for app settings in my opinion is for values that change with the target environment. Connection strings are a perfect example of this. In a TEST environment we would expect to talk to a different database than a PRODUCTION environment.
This is where app settings and Config Transformations come in very handy. One rule to decide is this: If your app setting is the same in every target environment, then it doesn't need to be an app setting.
What about Code Reuse?
Keeping values in one place is very useful. But it doesn't mean they belong in the app settings. Globally accessible static classes with Constant field variables is a perfectly acceptable way of maintaining consistency and adhering to the DRY principle.
When App Settings become a Feature
If we begin to update changing values on a regular basis then the overhead of updating unit tests and deploying can become a burden. At this point we have learned that the ability to update such settings needs to become part of the application. A discussion should be had with the Product Owner over the time spent redeploying versus time invested in providing a new feature to allow users to update values without requiring developer time.
Conclusion
App settings are a tempting place to put variables that we expect to change. However, it is more valuable to 'hard code' such values. This is so that we can make valid assertions against the business rules 'at present'. It is in our interest to break a test if this value changes, and know about it as soon as possible. We also know that we should be deploying changes exactly the same way - whether the changes are in the app settings or source code. This means a change to the app settings file is no more difficult or time consuming than it is to change the source code of our system. Target environment variables are the only valid use-case for app settings. This is to allow such values to vary (transform) between environments. App settings should only exist if the value changes between environments.