Just a note (which will probably get lost in the deafening roar that this thread now is) to say that the solution henser87 gave a few pages ago doesn't do quite what he said and is a bit too sledgehammery.
Moving/disabling all the ATI/AMD kexts as he described did not--in my case at least--force the system to use the on-chip Intel integrated graphics--rather it seemed to make my system use the Radeon 6750M card in a super-basic mode, like software-framebuffer style or something. Redraws were flickery and the system was barely usable. System Information.app showed the 6750M still active, and the Monitors seciton in System Preferences acted like my built-in display was an external monitor (plus gfxCardStatus, which I already had installed, reported the the discrete graphics were in use, and said I couldn't switch to integrated because "external monitor" was using the discrete card).
So, looking further back in this thread, user saramwrap said back on page 126 of this thread ( !?! ) to try disabling just ATIRadeonX3000.kext (or ATIRadeonX2000.kext, as your hardware case may be). This didn't quite work for me either--system still wouldn't boot. I'm guessing this was because I'm on Mavericks and that solution was back in Mountain Lion days. Anyway, I tried disabling more one by one, and seem to have gotten lucky on the first try. I have now disabled:
ATIRadeonX2000.kext
ATIRadeonX2000GLDriver.bundle
And voila! My system boots again, where it was going straight to a grey screen every boot previously. Scarily, while when I booted gfxCardStatus showed me on the integrated chip (yay!) when I launched Aperture, it said it had switched to the ATI card (yikes!), whereupon I promptly quit Aperture, switched gfxCardStatus to use integrated only, and now when I start Aperture it doesn't switch. So, for now, I think I'm back up and running with only integrated graphics...which thankfully I can live with for now, maybe until the Broadwell RMBPs come out. Till then I'll sit back and see if at this point in the wave of users having this problem if it finally triggers a response from Apple.
Oh yeah, add me to the list, yesterday my Late 2013 MBP i7-quad w/Radeon 6750M suddenly went all black-and-white lines on the screen, and then wouldn't boot again (grey screen) till I started messing with .kexts.
My output for `kextstat | grep AMD` now shows:
86 2 0xffffff7f810c9000 0x109000 0x109000 com.apple.kext.AMDSupport (1.2.0) <85 83 11 10 7 5 4 3 1>
87 0 0xffffff7f811d2000 0x212000 0x212000 com.apple.kext.AMD6000Controller (1.2.0) <86 83 11 10 5 4 3 1>
110 0 0xffffff7f81553000 0x3c3000 0x3c3000 com.apple.AMDRadeonX3000 (1.2.0) <109 83 11 7 5 4 3 1>
123 0 0xffffff7f81b9c000 0x24000 0x24000 com.apple.kext.AMDFramebuffer (1.2.0) <86 83 11 10 7 5 4 3 1>