I am not sure why you want to do this using recursion since a simple while loop would do what the same job but if you really want to do it in Java using Processing then the code below will do the same as your PHP.

I have made the following assumptions

1. When a value is taken from $input it reduces the number of values in it by 1. So-
2. When the recursive function has fully played out the $input will be an empty array
3. You want $input to behave like a LIFO (last in first out) stack

Unlike PHP variables in Java are statically typed and standard arrays are of fixed length so I have used a LinkedList instead of an array, this is neccessary because of assumptions 1 and 2. Since LinkedList gives access to bothe ends of the list it makes it easy to behave like a stack.

The array of Strings is there is simplify the task of populating the LinkedList.

1. String[] words = new String[] { "Mary", "had", "a", "little", "lamb" };
2. LinkedList<String> input = new LinkedList<String>();
3. int c;
4. 
   
5. void setup() {
6.   size(200,200);
7.   for(int i = 0; i < words.length; i++)
8.     input.addLast(words[i]);
9.    
10.    c = recursive_function(input, 0);
11.    println(c + " was returned by the recursive function");
12. }
13. 
    
14. int recursive_function(LinkedList<String> input, int count) {
15.   if(input.isEmpty()) {
16.     return count;
17.   }
18.   else {
19.     String word = input.removeLast();
20.     count++;
21.     println(word + "  " + count);
22.     return recursive_function(input, count);
23.   }
24. }

The output from this is


lamb  1
little  2
a  3
had  4
Mary  5
5 was returned by the recursive function

I noticed from that what my php function was missing was the return on count thank you. Thats why it was not working. I needed to do that to pass the result back out. 

Very true. Dually noted.