On the topic of learning C# language itself and the runtime, I would recommend the Learn C# section on the MSDN. There are links to lot of articles and trining materials abtou C#. You can combine this with Jesse Liberty's Learning C# 3.0.
On the topic of desktop programming, the answer depends on what platform you would like to use.
If you want to target WPF, I'd recommend Petzold's Applications = Data + Markup. (As a side note, learning WPF would give you the basis to learning about RIA with Silverlight)
If you want to target WinForms... well, I am biased and would recommend against. But if you insist, Petzold's Programming Microsoft Windows Forms is another good book. :-) Chris Sells' Windows Forms 2.0 Programming also is very good book about WinForms.
The WindowsClient.net Get Started and Learn sections have a lot of training videos, articles, FAQ and samples for both WinForms and WPF. The Community Books section also has an extensive list of books on both technologies.