I am new to WPF, and in every tutorial I read, they either have a [System.STAThread] attribute applied to their Main method, or they tell the reader to do that.
Is this attribute really "required"? And if so, why?
This is more a Windows requirement than a WPF one, and goes back to the original design of Windows forms and controls, from before .NET.
STAThread refers to "Single-Threaded Apartments" which refers to the threading model used by the current (main) thread. The threading model in use dictates how other .NET and COM applications will talk to your application (and inherently, its threads). The single-threaded application model requires that no single object "live in" more than one STA thread at a time, verses the MTA thread model; and allows for the passing of pointers to data across apartments only via marshalling-as-object.
Basically, with the [STAThread] declaration, other applications will know what your thread's policy is when sending you data. The STA model is the most common threading model for Windows threads/applications; but you'll sometimes come across certain code that won't run if called from an STA-modeled thread, because it's designed to send/receive data across thread boundaries in ways that don't comply with the STA restrictions. Knowing beforehand what the apartment model of a given thread allows the IDE to catch these exceptions at compile-time instead of getting nasty access violation errors when you attempt to use an object across thread boundaries during runtime.
You can read about STA and MTA threads from the MSDN article at: http://msdn.microsoft.com/en-us/library/ms680112(VS.85).aspx
Note that even normal .NET applications (from before WPF) required the [STAThread] declaration atop of the main().