One fix: Okay, this solution worked for me! For anyone having problems, if you have forced anything in the AMD CCC like anti-aliasing or tessellation, try turning the settings to "Use application settings" instead. My FPS went from 20-30 to an almost constant 60 on Ultra settings with the official HD texture pack. If you have a Nvidia card, use the NCP and see if you've forced anything like I mentioned for the CCC. I hope this helps.
Thanks to deaths_soul for figuring this out!

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Possible fix: Disable the HD texture pack (if you have it installed).
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Possible fix: Delete your .ini and .pref file in your Documents/My Games/Skyrim folder
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Possible fix: Disable mouse acceleration
- Go to \Users\[Username]\My Documents\My Games\Skyrim
- Open the SkyrimPrefs.ini file with notepad
- Find the line bMouseAcceleration=1 (located under [Controls])
- Replace the 1 with a 0
- Save the file (make sure you don't accidentally save it as Skyrim.ini.txt)
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Possible fix: If using an ATI card, install the latest 12.2 preview drivers
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If anyone finds any other solutions, private message me and I'll edit this post with it. Thanks!
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I've been getting suttering since 1.4, but before, when people seemingly had more problems, I ran the game perfectly fine.
It looks to be happening when I move, for some reason. When I stay still, my FPS is fine and everything, but when I move, I get this weird stuttering, not too bad sometimes, but incredibly annoying at other times. I used to be able to play the game on Ultra fine, but now even on High I get this stutter. Does anyone have any fixes?
Specs:
Intel i5 2500k 3.3Ghz
Radeon HD 6870
4GB Ram
Windows 7 64bit

Really svcks. Are you running constant 60 fps??
)