On the one hand, the answer is none. It is perfectly possible and reasonable to learn Silverlight as your first programming experience. But…to paraphrase David Platt , it is also possible to have an appendectomy through your mouth: it just takes longer and hurts more.
The truth is that right now our learning material is targeted at existing .NET programmers, and we more or less assume you have some familiarity with
DHTML (the fundamentals)
Basic programming concepts (conditionals, event handlers, etc.)
For the 1.1 material, we also assume you have some familiarity with the .NET CLR, managed code and C# or VB.
Finally, some of the videos do assume you've worked with ASP.Net, but only some.
So, to answer specifically:
ASP.NET: not necessarily (always a good skill to have, but not needed here unless you want to marry the two technologies)
XML: No, unless you have specific need of it
You didn't mention XAML and that is something you will need to know. XAML is the markup language for Siilverlight, and it is closely related to XML. But I believe you can learn XAML without first learning XML, with no problem. You can do so from the help files, from our videos and white papers, or from any of the very good books on Windows Presentation Foundation (WPF) which also uses XAML (the XAML used in Silverlight is a subset of the XAML used in WPF). I recommend 3 WPF books on my web site, so you might want to try one of those,
Hope that helps.