UPDATE: It seems some of this might need a little bit more detail and it also seems that some different Service Packs might respond differently. I have tested this on Windows XP (SP3) and Windows 7. Here are some more detailed instructions:
Step 0. Ensure that within iTunes you have unchecked “Sync Automatically” and under Edit -> Preferences, Devices, choose Prevent iTunes from syncing with Devices Automatically.
1. Ensure that your iPhone is on. You can see your Springboard. Plug your iPhone into your computer and ensure that iTunes recognizes it and preform a sync/backup/update.
2. Once you have completed this, close iTunes completely. Press the start button and choose Run. Press Ctrl+Alt+Del and check your task manager to ensure that any iTunes processes are closed, such as iPodService.exe, iTunesHelper.exe, etc. These must be turned off.
3. Ensure that your copy of blackra1n.exe is located in C:\blackra1n.exe.
4. Right click blackra1n.exe. If running Windows 7 choose properties, and then compatibility. Choose to run in Windows XP SP3 Mode.
5. Right Click blackra1n.exe and choose Run As. Chose the Administrator account and enter in the password.
6. Once blackra1n.exe is running, click Make it Ra1n.