The Windows SDK for Windows 8 (aka Windows 8.0 SDK) RTM version is now available on MSDN. See Where is the DirectX SDK? for details on DirectX content in the Windows 8.0 SDK. This includes the D3DCompiler_46.DLL release of the HLSL compiler, DirectXMath version 3.03, DirectX 11.1 headers/libs, and the GDF tools.
The Windows 8.0 SDK is included with Visual Studio 2012 (build 50727.1), which is now available on the web. See the Visual Studio and VC blog announcements for more information, as well as the ReadMe.You can find a list of compiler bugs fixed, Standard Library bugs fixed, and MFC bugs fixed for Visual Studio 2012 as well. As noted on the VC Blog, support for targeting Windows XP with VS 2012 and the Desktop Express edition will be coming soon. The Visual C++ 2012 CRT redistributable packages are on MS Downloads.
Note that the RTM version of Windows 8 (build 9200) is available for download for developers with an MSDN Subscription or TechNet Professional Subscription. General availability will be on October 26, 2012. For developers of Windows Store apps (a.k.a. Metro style apps), details on migrating your application to the RTM version are covered in this migration guide. There was a change to the CSRR rating system between the Release Preview and RTM as well.
Update: VS 2012 Express for Windows Desktop is now available. Support for Windows XP is available with VS 2012 Update 1. See also VS 2012 Update 2, VS 2012 Update 3, and VS 2013 and Windows 8.1 SDK RTM.
System requirements: The Windows SDK for Windows 8 can be installed on Windows 7 and Windows 8. It's the same system requirements as Visual Studio 2012 which includes the new Windows SDK. You need Windows 8 to develop Windows Store apps, but you can use Windows 7 and the Windows SDK 8.0 for development of Win32 desktop applications for Windows 8, Windows 7, Windows Vista, and their Windows Server equivalents.
VS 2010 users: You can use the property sheets as described in the Visual C++ Team blog post to use the Windows 8.0 SDK. The .props files are attached to this post as well. Note you cannot target Windows XP with the Windows 8.0 SDK.
The VS team's instructions omit including the "include\winrt" directory under the assumption that those are for Windows Store apps only, but that's not strictly true. At a minimum, having access to #include <wrl/client.h> provides you the extremely useful Microsoft::WRL::ComPtr smart-pointer that works perfectly fine in Win32 desktop apps and down-level systems.
Direct3D Debug support: Installing VS 2012 or the Windows 8.0 SDK also installs the Direct3D 10.x and Direct3D 11.x SDK Debug Layers on Windows 7, Windows 8.0, and the Server Equivalents for using D3Dxx_CREATE_DEVICE_DEBUG. Note that this is not the correct version for Windows 8.1, see Visual Studio 2013 and Windows 8.1 SDK RTM are now available.