I just saw an interview with Luca Bolognese from the MS language team, and he mentioned that Anders Hejlsberg thinks developers should focus more on the BCL (base class library, framework) instead of lanugage features (C#, VB.NET).
Which class or interface in the current .net 3.5 framework should every developer know?
This isn't a class, but if you're talking about 3.5 framework essentials then IQueryable is important to know.
The classes in System.Reflection and System.Diagnostics are quite powerful pieces of the framework that nobody seems to know.
If you're talking about .NET 3.5 specific classes, The LINQ extension methods in the static Enumerable class are (IMHO) the most important.
Depending on WHAT you want to develop. I think most of us only (and only needs to) know parts of the whole framework.
Not 3.5 specific, but I would suggest two classes that gives for free what many writes code to solve: System.IO.Path (OregonGhost beat me by a few seconds on that one...) and System.IO.File. One underused gem in here is the method Path.Combine.
And also EventHandler<T>, instead of defining your own event delegates.
IDisposable and most of System.Collections.Generic spring to mind...