How can I stop the Windows cursor from appearing over Skyrim? [duplicate]

You might want to try SKSE: http://skse.silverlock.org (installer)
It makes it easy to "mod" skyrim and use certain fixes.

SKSE: The Skyrim Script Extender, or SKSE for short, is a modder's resource that expands the scripting capabilities of Skyrim. It does so without modifying the executable files on disk, so there are no permanent side effects. Source: http://skse.silverlock.org/skse_readme.txt

There is a certain mod that may fix your problem which requires SKSE : http://www.nexusmods.com/skyrim/mods/36125/?

It's perfectly safe.

I think that using the SKSE launcher already resolved the problem with cursors for me. However installing that extra plugin may be required for you.

It is always possible that your problem is the one mentioned in the other answers.

Extra note: I instantly had 2 cursors no matter if I alt-tabbed or not.

Running (shift)(W) while strafing (A) and then jumping (space) will key-jam most keyboards.

Key Jamming:

Key ghosting occurs on matrix keyboards for certain combinations of three keys. When these three keys are pressed simultaneously a fourth keypress is erroneously registered by the keyboard controller.

Solution (fullmooninu's answer):

Press ESC, save a new game file (leave the main game menu open). ctrl-alt-del to open task manager. Close taskman and go back to the game.

As with all Creation engine games, wait a few seconds before you touch anything, even after it has seemingly resumed. (I try to stop walking if I know it's loading cells; if you hear your HD spinning up, take a breather.)

Sticky Keys is triggered by pressing the shift key multiple times in succession, which doesn't sound like what you are doing. A related but slightly-less-known feature is Filter Keys, which is triggered by holding down the shift key for eight seconds.

I suspect this is why you are hearing the beep and seeing the cursor, so you should turn off Filter Keys as well. You can turn off Filter Keys and the related keyboard activation shortcuts from the Ease of Access Center in the Control Panel. Alternatively you can activate Filter Keys while in explorer (hold right shift for eight seconds) and the resulting post-beep dialog will have a link to take you directly to the relevant control panel and disable the option.

This problem drove me crazy also. Found a mod on the Nexus that absolutely works. Instead of trying to hide the cursor, as most others do, it disables the background cursor while the game is running. I've had absolutely zero problems since installing, and it has other advantages also. Get it here: http://www.nexusmods.com/skyrim/mods/40706/?tab=4&&navtag=http%3A%2F%2Fwww.nexusmods.com%2Fskyrim%2Fajax%2Fcomments%2F%3Fmod_id%3D40706%26page%3D1%26sort%3DDESC%26pid%3D0%26thread_id%3D1083255&pUp=1 It requires SKSE, but actually works!