I purchased a top of the line 24" iMac about a year and a half ago to replace an out-of-warranty 17" iMac that was suffering from a fried logic board and possibly power supply. The new iMac served me well up until a month ago when the display decided to turn off in the middle of a game of Warcraft. The computer itself seemed to be functional, as iTunes was still playing in the background, but nothing would make the screen turn back on (which, on the upside, meant that I avoided the messages of "omg u noob! move ur units idiot or ill ban you" etc). The display came on about a half hour later while I wasn't even using the computer, but must've misinterpreted the 'once you go black' expression, because as soon as I came back over it shut off again and wouldn't come back on.
The next day I packaged it up and brought it over to my local Apple store, which unfortunately involved schlepping the 40 pound box through the mall and waiting several minutes for the elevator due to the large contingent of people who apparently needed to use the elevator rather than the stairs to go down one level to the food court and thought that the guy with the big-ass computer box should wait...but I digress. After arriving at the Apple store and waiting for some guy with an amazingly somewhat functional PowerBook G3 (

A few days later I came to pick up my machine, hauled it back through the mall, drove the 45 minutes back home, hauled it up the stairs to my apartment, set it up on my desk, and started using it. A few minutes later it occurred to me that I probably should've tested it in the store. You see, the technicians at the Apple store had apparently replaced the video card with one that instead of shutting off induced Flash-o'-Death syndrome. My computer would now usually stay on for about one to five minutes before the screen would brightly flash once and the computer would completely freeze, display and all. In addition, the screen would occasionally exhibit rainbow-colored static across the bottom part of the screen that looked pretty cool but signaled the impending death of whatever I was trying to do at the time. So the next day I packaged it up again, drove back to the mall, hauled it to the Apple store, and detailed my story, complete with low-quality videos shot from my laptop's webcam of my iMac crashing and burning. The genius didn't seem to have any great ideas as to what the problem was other than possibly the logic board, but told me that since I'd already brought my computer in they'd bump it to the front of the repair queue and get back to me in a few days. He looked at me weird when I told him that I'd changed my randomly generated 11-digit admin password from last time, but took down my new one after checking that I hadn't also changed the login name.
Close to a week later after making several phone calls trying to get information, all I found out what that they'd replaced the logic board and it hadn't fixed the problems. Doing all my work on a 13" laptop in the meantime was getting pretty old, so I took this as a cue to hope that they'd fail to fix the problem and offer me a shiny replacement instead. To my disappointment, they phoned me a day later to tell me that they'd replaced 1) the logic board, 2) the power supply, and 3) the graphics card (again) and that the computer was now working just fine. So I made the 4th trip to the mall, brought my computer back, and started using it. Apart from the annoyance that they'd changed my admin password and reset my open firmware password (maybe the genius took down my second password wrong?), the computer itself seemed to be functional again.
All was well for about two weeks. Until a few days ago, when I decided to try out Warcraft again and my display remembered what that was a cue for and turned itself off. A few minutes later the computer froze. After rebooting, it lasted about 15 minutes before deciding that opening a PDF was too much strain and froze again. At that point I'd had enough of computer surgeries (and the top of my box was starting to wear out from being used so much) so I called AppleCare for the third time and told the guy I wanted a replacement. He told me that it was standard policy to only offer a replacement after 3 repairs, though I pointed out that each repair had apparently failed to fix the underlying problem. He went and talked to his supervisor before coming back and repeating the same thing back to me ("go wait for an unknown period of time to have it repaired again, then call us if there are any further problems"). I told him to connect me to customer relations, which got me on the phone with a friendly woman who told me she'd go talk to somebody and see if an exception could be made. A few minutes later, she came back on and told me that they'd like me to have it 'repaired' again. I was pretty close to giving up at that point, but stayed on the phone for a bit to protest, note how poorly my AppleCare support experience was going, and so forth. After a while she agreed to go talk to another unknown party and see if anything could be done. And finally, after a 5th time on hold, she came back and told me they could offer me a shiny new 27" iMac as a replacement. She even let me pay a little money to upgrade to the quad-core version and threw in the Core i7 upgrade for free.
So that's pretty much my story. I'm waiting for my vastly superior new machine to arrive in the mail, at which point I'll be able to fedex off my old box and not have to haul it around anymore. Obviously I consider my AppleCare a $120 well-spent (ooh, a moral! buy your AppleCare, kids) and am now quite satisfied with my support experience.
Of course, a topic isn't really a topic unless more than one person has something to post about, so I invite you all to regale us with tales of all things received for free. Especially those which involve blood, sweat, and tears to receive.