Agree with HeartlessBtch. "How" a man looks at a woman is very important.
If you want to come off as a creepy dude, keep staring at women for long periods of time.
If you want to come off as a sleazy, disrespectful, ghetto fool, keep looking at women's tits and ass.
If you want to come off as a normal, decent, "qualifying" guy, the best way to look at a woman might be to just take occasional glances at her. If she catches you, go ahead and smile at her to signal that you're digging her.
If you're going to play the "ignoring" game, good luck. A woman will notice you regardless of whether you're looking at her or ignoring her if she thinks you're attractive. But if your looks are not that noticable to begin with, it might be better to actually look at her and hopefully catch her eye and smile at her.