It's definitely possible to develop apps that do not follow the MVVM or MVC patterns. You can develop your apps however you like; these are merely architectural patterns that many programmers follow when developing Windows Phone apps. MVVM, in particular, is suited to Windows Phone app development (and WPF) because of the data binding mechanism provided by XAML.
For example, you might choose to write your code entirely in code-behind (*.xaml.cs) files and subscribe to events directly on the view. This might be fine for small apps, but may not be suitable for larger apps, especially when there are multiple people working on different parts of the app (e.g. a designer working in XAML and a coder working in C#) and when testability is extremely important.
I won't provide links to learning materials for MVVM/MVC; a mere bing search results in an abundant amount of information at your fingertips. Good luck!
