Hiding inherited members

Override them like Michael Suggests above and to prevent folks from using the overridden (sp?) methods, mark them as obsolete:

[Obsolete("These are not supported in this class.", true)]
public override  void dontcallmeanymore()
{
}

If the second parm is set to true, a compiler error will be generated if anyone tries to call that method and the string in the first parm is the message. If parm2 is false only a compiler warning will be generated.

I think you're best least hackish way is to consider composition as opposed to inheritance.

Or, you could create an interface that has the members you want, have your derived class implement that interface, and program against the interface.

One potential thing you can do is contain the object rather than extend from the other class. This will give you the most flexibility in terms of exposing what you want to expose, but if you absolutely need the object to be of that type it is not the ideal solution (however you could expose the object from a getter).

Thus:

public class MyClass : BaseClass
{
    // Your stuff here
}

Becomes:

public class MyClass
{
    private BaseClass baseClass;

    public void ExposeThisMethod()
    {
        baseClass.ExposeThisMethod();
    }
}

Or:

public class MyClass
{
    private BaseClass baseClass;

    public BaseClass BaseClass
    {
        get
        {
            return baseClass;
        }
    }
}

While you cannot prevent usage of those inherited members to my knowledge, you should be able to hide them from IntelliSense using the EditorBrowsableAttribute:

Using System.ComponentModel;

[EditorBrowsable(EditorBrowsableState.Never)]
private string MyHiddenString = "Muahahahahahahahaha";

Edit: Just saw this in the documentation comments, which makes it kinda useless for this purpose:

There is a prominent note that states that this attribute "does not suppress members from a class in the same assembly". That is true but not complete. Actually, the attribute does not suppress members from a class in the same solution.