Monkey Island: The Head of the Navigator

Python, 224 + 97 + 1 = 322 characters

A most straightforward solution to start us all off. Thanks to gnibbler for helping me shave off 18 bytes!

n=0
print open('z','rb').read().decode('zip').split('|')[n]
open(__file__,'r+').write("n="+`n+1`)

Requires the file z to be present in the same directory (+1 for filename, +224 for file size):

$ hexdump z
0000000 9c78 d1ad 6e3d 30c3 050c bde0 78a7 165b
0000010 0723 92c8 48a9 b43a 8209 192c 9b29 0491
0000020 a2ab 9fa1 021a f87a 715a f46c d100 1026
0000030 1efc 1e41 5172 4721 c3b3 1527 607c 4c70
0000040 6191 87e8 0c91 7825 7b6e 2d47 dfef 4c8e
0000050 0edd d25f e540 8b54 8fbe 4bb8 c500 7ade
0000060 288d c418 c4d9 6cae 0f7f 7bab 6832 9be5
0000070 be21 7aa9 537d c2c2 24dd 25a3 c50f e41a
0000080 ca1c 1ff4 a7c9 a439 d5cc 9a4d b207 3fe9
0000090 0e7c 529c 4e79 3afc 7cef bf79 6f5e 672f
00000a0 8b9f 6d1d 8832 5359 1698 2482 92c3 3270
00000b0 43cd 560e 899b a4ad 1ab2 548a aed9 0bf1
00000c0 238f 0697 bd63 168f 36e9 b411 0a1e fef6
00000d0 eee8 1d64 1a28 aec9 10e3 7ff7 3a0b d9ab
00000e0

$ ls -l z
-rw-r--r--+ 1 Laxori mkpasswd 224 2014-09-22 22:35 z

You can generate z with the following:

>>> open('z','wb').write("""eJyt0T1uwzAMBeC9p3hbFiMHyJKpSDq0CYIsGSmbkQSroqGfGgJ6+FpxbPQA0SYQ/B5BHnJRIUez
wycVfGBwTJFh6IeRDCV4bntHLe/fjkzdDl/SQOVUi76PuEsAxd56jSgYxNnErmx/D6t7MmjlmyG+
qXp9U8LC3SSjJQ/FGuQcyvQfyac5pMzVTZoHsuk/fA6cUnlO/DrvfHm/Xm8vZ5+LHW0yiFlTmBaC
JMOScDLNQw5Wm4mtpLIailTZrvELjyOXBmO9jxbpNhG0Hgr2/ujuZB0oGsmu4xD3fws6q9k=""".decode('base64'))

Output:

$ python monkeyisland.py
Guybrush: May I please have that necklace?
Head: No, but thanks for asking so politely.
$ python monkeyisland.py
Guybrush: Oh come on, pleeeeease?
Head: You can beg all you want, but you can't have it.
$ python monkeyisland.py
Guybrush: Pretty please?
Head: You can beg all you want, but you can't have it.
$ python monkeyisland.py
Guybrush: Pretty PRETTY please?
Head: You can beg all you want, but you can't have it.
$ python monkeyisland.py
Guybrush: Pretty please with sugar on top?
Head: Oh, all right, you big baby. You can have it. Hey, what good's a necklace if you don't have shoulders?
$ python monkeyisland.py
Traceback (most recent call last):
  File "monkeyisland.py", line 2, in <module>
    print open('z','rb').read().decode('zip').split('|')[n]
IndexError: list index out of range

Common Lisp (SBCL) : 659 characters

(defparameter *d*
  '#1=("~A May I please have that necklace?"
       "~A No, but thanks for asking so politely."
       "~A Oh come on, pleeeeease?"
       #2="~A You can beg all you want, but you can't have it."
       "~A Pretty please?"
       #2#
       "~A Pretty PRETTY please?"
       #2#
       "~A Pretty please with sugar on top?"
       "~A Oh, all right, you big baby. You can have it. Hey, what good's a necklace if you don't have shoulders?" . #1#))
(defun d ()
  (format t (pop *d*) "Guybrush:") (terpri)
  (format t (pop *d*) "Head:") (terpri)
  (terpri)
  (finish-output)
  (sb-ext:save-lisp-and-die "please" :toplevel 'd :executable t))
(d)

Explanations

• I dump the lisp image after each invocation, which saves current state.
• The circular list let me restart the dialogue after all lines have been displayed (not required, but at least it doesn't error on format with nil).
• Reader macros allow me to reuse some identical lines.

This won't be the shortest submission, but I thought this was a nice approach to the problem.

Firt invocation

 $sbcl --noinform --noprint --load please.lisp
 Guybrush: May I please have that necklace?
 Head: No, but thanks for asking so politely.

 [undoing binding stack and other enclosing state... done]
 [saving current Lisp image into please:
 writing 5856 bytes from the read-only space at 0x0x20000000
 writing 4032 bytes from the static space at 0x0x20100000
 writing 67960832 bytes from the dynamic space at 0x0x1000000000
 done]

Subsequent invocations

$./please 
Guybrush: Oh come on, pleeeeease?
Head: You can beg all you want, but you can't have it.

[undoing binding stack and other enclosing state... done]
[saving current Lisp image into please:
writing 5856 bytes from the read-only space at 0x0x20000000
writing 4032 bytes from the static space at 0x0x20100000
writing 68091904 bytes from the dynamic space at 0x0x1000000000
done]

$./please 
Guybrush: Pretty please?
Head: You can beg all you want, but you can't have it.

[undoing binding stack and other enclosing state... done]
[saving current Lisp image into please:
writing 5856 bytes from the read-only space at 0x0x20000000
writing 4032 bytes from the static space at 0x0x20100000
writing 68091904 bytes from the dynamic space at 0x0x1000000000
done]

C# - 593 + 1 + 1 Characters (595)

Edits: Updated with suggestions from Martin and various other optimisations

First +1 is a filename. Second +1 is contents of that file. Without all the spaces and line breaks removed so you can read it:

using System.IO;
using s=System.String;
class P
{
    static void Main()
    {
        s g="Guybrush: ",h="Head: ",p=" please",q="Pretty";
        s[]b=new s[]{"May I"+p+" have that necklace","No, but thanks for asking so politely.",
        "Oh come on, pleeeeease","You can beg all you want, but you can't have it.",q+p,
        "Oh, all right, you big baby. You can have it. Hey, what good's a necklace if you don't have shoulders?",
        q+" PRETTY"+p,"",q+p+" with sugar on top"};
        int a=int.Parse(File.ReadAllText("x",System.Text.Encoding.UTF8));
        System.Console.WriteLine(g+b[a]+"?\n"+h+b[(a+5)/6*2+1]);
        File.WriteAllText("x",(a+2).ToString());
    }
}

Explanation

Relies on a text file called "x" to be present in the directory. Should initially contain a zero and is used to store progress.

Program plucks relevant element out of the string array according to progress and writes progress at end. Some lines reused to shorten length, hence index selection logic h+b[(a+5)/6*2+1] for answer selection.

Output

D:\Projects\Junk\MI\bin\Debug>MI
Guybrush: May I please have that necklace?
Head: No, but thanks for asking so politely.

D:\Projects\Junk\MI\bin\Debug>MI
Guybrush: Oh come on, pleeeeease?
Head: You can beg all you want, but you can't have it.

D:\Projects\Junk\MI\bin\Debug>MI
Guybrush: Pretty please?
Head: You can beg all you want, but you can't have it.

D:\Projects\Junk\MI\bin\Debug>MI
Guybrush: Pretty PRETTY please?
Head: You can beg all you want, but you can't have it.

D:\Projects\Junk\MI\bin\Debug>MI
Guybrush: Pretty please with sugar on top?
Head: Oh, all right, you big baby. You can have it. Hey, what good's a necklace
if you don't have shoulders?

D:\Projects\Junk\MI\bin\Debug>

My first code golf, probably not the shortest possible in C# but hey - Monkey Island, couldn't resist!

Stripped code:

using System.IO;using s=System.String;class P{static void Main(){s g="Guybrush: ",h="Head: ",p=" please",q="Pretty";s[]b=new s[]{"May I"+p+" have that necklace","No, but thanks for asking so politely.","Oh come on, pleeeeease","You can beg all you want, but you can't have it.",q+p,"Oh, all right, you big baby. You can have it. Hey, what good's a necklace if you don't have shoulders?",q+" PRETTY"+p,"",q+p+" with sugar on top"};int a=int.Parse(File.ReadAllText("x",System.Text.Encoding.UTF8));System.Console.WriteLine(g+b[a]+"?\n"+h+b[(a+5)/6*2+1]);File.WriteAllText("x",(a+2).ToString());}}