I’m currently a full time .NET developer, and I find having a background in C to be rather helpful. I recently went back and “relearned” C since I never really “got” it the first time around, and noticed that the concepts have helped me out while writing C#. Specifically, I have a much better understanding of when to pass objects by value or reference, and delegates. It’s probably not absolutely mandatory to understand C, but all of the best C# developers I know do.
Of course, I very much prefer a GC’ed environment than one without, and I would rather poke myself with a hot iron than create a full application in just C.