The ActionController::RoutingError is a prevalent issue in Ruby on Rails projects, akin to the 404 error in web applications, indicating that no route matches the URL entered by the user. This error arises when the ActionController, which acts as the intermediary in the Model-View-Controller pattern, cannot find a suitable path for a request. To handle this error, developers can implement a catch-all route in the config/routes.rb file and define a not_found_method in the ApplicationController to render a 404 page. Running the command "rails routes" helps identify missing routes, which can then be added to the configuration. Additionally, deploying applications on platforms like Heroku may lead to routing errors due to static file serving issues, which can be resolved by enabling public file server configuration in the production environment. Tools like Rollbar can aid in tracking, analyzing, and managing errors in real-time, providing a more confident approach to deploying production code.