<p>What are the alternative "design methods" to the Model View Controller? MVC seems to be popular (SO was built with it, I know that much) but is it the only method used?</p>

There are many others:
Model View Presenter (MVP)
Supervising Controller
Passive View
Model View ViewModel (MVVM)
This is common in WPF applications (though
Prism
uses the MVP pattern (usually))