Faint flickering on screen when playing games in windowed mode?

I've actually had this problem for at least a year or more, but has started to become much more noticeable in certain games. Pretty much any time I start up a graphically-intense game and play it in Windowed mode, I get these lines that seem to flicker across the screen. They're not in-game, but appear to be on top of everything, as if just under the screen. It will easily overlap the...