Assume that the list is in column A, starting at row 1. In cell B1 you can enter:
=COUNTIF(A1,A1)
Which will of course give 1. (Or you can just enter a hard-coded value of 1, it's up to you.)
In cell B2, enter the formula
=COUNTIF($A$1:A2,A2)
and copy that down for the rest of your list. NOTE CAREFULLY the fact that the cell at the start of the list ($A$1) is absolute, and the end of the list (in this case A2, though that will change as you copy the formula down the rows) is relative. What you're essentially doing is counting up the number of matching items from the start of the list, down to and including that row. So cell B5 will return 2, since there are 2 Donkeys between $A$1 and A5. Cell B6 will return 3, since there are 3 Donkeys between $A$1 and A6, and so on.