There are, of course, countless examples of this, especially if one spends anytime in comments sections (the bane of good thinking) of any number of websites. One of the more frequent arguments I come across, not just online but in the Real World, is from atheists who say something along the lines of, "There is no proof that God exists, therefore he doesn't."
This is a fine example of argumentum ad ignorantium often phrased as "absence of evidence is not evidence of absence." If you want to have a serious debate with someone, you should at least attempt to formulate a well-reasoned, logical basis for your proposition. Otherwise you're just shouting nonsense. And, yes, I realize that thinking people might use more reason and logic is, well, illogical; but I think it's a worthy cause. There's nothing wrong with not believing in God, but you can certainly make your case using good logic. Teachers, I know you're just sitting on your lazy butts, so how about adding some logic to the curriculum, eh?*
*I'm just kidding, teachers. That was an example of sarcasm. Maybe you could teach your students how to detect that after the logic lesson.