gistfile1.cs

public interface IFoo
{
   void Foo();
}

public class Base:IFoo
{
   public void Foo()
   {
   }
}

public class Inherited: Base,
                        IFoo // <-- why/when would you want to do it?
{
}

Never, it is redundant. ReSharper suggests to remove line 14.

If you would use reflection then under certain circumstances it could be handy.

And if you would like to implement the interface explicitly.

I can't think of a single reason to do this. Even if you can come up with some technical corner case where it may seem necessary (e.g. explicit interface implementation) it violates the Principle of Least Astonishment, so is a design smell. If you need to override the behavior of Foo, make it virtual in Base. If you don't own Base, create a Decorator instead of deriving from Base.

Yes, this is design smell and I would never use them. I wrote just technical reason why someone would want to do it :-)