I was given the "opportunity" to salvage several projects and executives replaced the entire dev team because the app had too many errors and the users were tired of the problems and run-around. These code bases all had centralized error handling at the app level like the top voted answer describes. If that answer is the best practice why didn't it work and allow the previous dev team to resolve issues? Perhaps sometimes it doesn't work? The answers above don't mention how long devs spend fixing single issues. If time to resolve issues is the key metric, instrumenting code with try..catch blocks is a better practice.
How did my team fix the problems without significantly changing the UI? Simple, every method was instrumented with try..catch blocked and everything was logged at the point of failure with the method name, method parameters values concatenated into a string passed in along with the error message, the error message, app name, date, and version. With this information developers can run analytics on the errors to identify the exception that occurs the most! Or the namespace with the highest number of errors. It can also validate that an error that occurs in a module is properly handled and not caused by multiple reasons.
Another pro benefit of this is developers can set one break-point in the error logging method and with one break-point and a single click of the "step out" debug button, they are in the method that failed with full access to the actual objects at the point of failure, conveniently available in the immediate window. It makes it very easy to debug and allows dragging execution back to the start of the method to duplicate the problem to find the exact line. Does centralized exception handling allow a developer to replicate an exception in 30 seconds? No.
The statement "A method should only catch an exception when it can handle it in some sensible way." This implies that developers can predict or will encounter every error that can happen prior to release. If this were true a top level, app exception handler wouldn't be needed and there would be no market for Elastic Search and logstash.
This approach also lets devs find and fix intermittent issues in production! Would you like to debug without a debugger in production? Or would you rather take calls and get emails from upset users? This allows you to fix issues before anyone else knows and without having to email, IM, or Slack with support as everything needed to fix the issue is right there. 95% of issues never need to be reproduced.
To work properly it needs to be combined with centralized logging that can capture the namespace/module, class name, method, inputs, and error message and store in a database so it can be aggregated to highlight which method fails the most so it can be fixed first.
Sometimes developers choose to throw exceptions up the stack from a catch block but this approach is 100 times slower than normal code that doesn't throw. Catch and release with logging is preferred.
This technique was used to quickly stabilize an app that failed every hour for most users in a Fortune 500 company developed by 12 Devs over 2 years. Using this 3000 different exceptions were identified, fixed, tested, and deployed in 4 months. This averages out to a fix every 15 minutes on average for 4 months.
I agree that it is not fun to type in everything needed to instrument the code and I prefer to not look at the repetitive code, but adding 4 lines of code to each method is worth it in the long run.