Don't abuse this how-to, but if regular Applecare can't get you the satisfaction you deserve—or think you deserve—here's how to get in contact with people who have the power to do anything (within reason).
1) Call Apple Corporate: 408-996-1010)
2) Ask the operator for Gene (like denim) Teluse, VP of Customer Care. She is Apple's highest ranking customer service agent, and she reports directly to Steve Jobs.
3) Leave a nice message, include any Apple Case/Repair numbers you might have, or your machine's serial number, and a callback number.
4) Wait ~24 business hours for one of Ms. Teluse's minions to call.
5) Calmly explain your story, and what you want Apple to do.
Tipster Thirdgen adds that in general, Apple will not replace a machine unless it has been unsuccessfully fixed 3 or more times for the same issue, or several major repairs (i.e. a logic board, a screen, a top case as separate repairs).
Only use this if you've jumped through various hoops and still can't get your Apple machine repaired. Don't use this if you've just dropped your iPod in the toilet and you hope they can send you a replacement "just cause".
Get Applecare Executive Customer Service [Consumerist]