I see a bigger issue than that!
vb Code:
  1. ListBox1.Items.Add(intArray(howmany))

Howmany is the number that people are entering, not an index value. What you need is:

vb Code:
  1. Dim intArray(19) As Integer
  2.         Dim howmany As Integer
  3.         Dim count As Integer
  4.  
  5.         For count = 0 To 19
  6.             'GET VALUE THAT USER ENTERS
  7.             howmany = CInt(InputBox("Please input how many fish " & ControlChars.CrLf _
  8.             & "you caught on each trip."))
  9.  
  10.             'ASSIGN THE VALUE HOW MANY TO YOUR intARRAY AT THE CURRENT POSITION (0, then 1, then 2 etc...)
  11.             intArray(count) = howmany
  12.  
  13.             'Place CURRENT intArray value into Listbox - it's the count index that tells us that
  14.             ListBox1.Items.Add(intArray(count))
  15.  
  16.             'NO NEED FOR 'COUNT += 1'
  17.         Next count