I do not find short-circuiting to be useful in every case. I use it only when required. For instance, when checking two different and unconnected variables, it would not be required:
  If x > y And y > z Then
  End If
As the article by Paul Vick illustrates (see link provided by Ken Browning above), the perfect scenario in which short-circuiting is useful is when an object has be checked for existence first and then one of its properties is to be evaluated.
  If x IsNot Nothing AndAlso x.Someproperty > 0 Then
  End If
So, in my opinion both syntactical options are very much required.