Is your DirecX up to date? Are there any game updates that you didn't reinstall? Are all your Windows updates current as well as internet explorer?
If you can play some games normal and others not normal then it sounds like some kind of software issue , a hardware issue would be all the time and it wouldn't matter what game you played.
I have been experiencing the same problem for quite some time and I figured out that:
-this problem has apparently nothing to do with graphic card or graphic drivers (same symptoms with different cards and drivers),
-stuttering appears when in-game fps drops below the value of 60 nad goes worse with every lost frame (30 fps seems unplayable, even in games like Minecraft),
- it has to do with quality of your screen and cable attached.
To sum up, first try changing the video cable and if it not works as planned, try using different, better quality screen. HDMI or DVI plug can be the problem, so try changing between screens that are using them.
It is relevant to add, that I haven't figured out my problem yet - I am borrowing friend's screen to try it out soon (will post the result). It seems to happen mostly to the 1920x1080 60 Hz screens.