I have a SyncMaster 930B, and a PNY 9500 GT graphics card. I've seen horizontal lines, and really hard to see cutscenes within games, but movies play fine on the monitor. I've seen this issue before on my 7900GS as well. How do I tell if it's my video card or my monitor that's to blame? Monitor is about 4 or so years old.
It's a sad fact that just about all PC games ignore vertical blanking. On other platforms, vertical blanking is (or, at least, used to be) considered a major part of getting smooth video animation. A frame would be rendered, but kept until a VBI (vertical blanking interrupt) was triggered. This is when the monitor finishes drawing a frame (or field), and is busy preparing itself to draw a new one. At that point, the interrupt handler would quickly swap the visible frame, and suddenly the monitor gets the right frame at just the right time. Without this you get "tearing" of the image, as half of one image might be drawn, and suddenly, as the monitor is halfway through, the next frame is swapped in, which has a slightly different view of the scene, since things are (probably) moving. In cutscenes, where big movements and pans happen, and you're not focusing on the action of your character or an enemy, but the whole image, this is more obvious.
The upshot is: if you want proper, smooth video animation in PC games, you probably want to go to your video card's settings and enable vertical sync (or whatever your particular settings program calls it).
I'm not sure how relevant it is these days with flatpanel monitors, but I presume it should still be better in principle than flipping at random times whenever a frame finishes drawing.