Here's a puzzle "classic". I call it the infamous brick puzzle, and you'll see why.
There are actually two variations on this puzzle.
Variation 1:
Draw a curve without lifting your pencil such that you pass exactly once through the top, bottom, right, and left sides of each of the five rectangles. No passing through corners.
Variation 2:
Draw a curve without lifting your pencil such that you pass through each line segment exactly once. Note that the lower left and lower right rectangles each have 4 line segments surrounding them, while all the others have 5. Again, no passing through corners
There are a lot of stories I've heard of people obsessing over this puzzle, trying to find the solution. Once I read a story by this guy who was given this puzzle in elementary school, and he obsessed over it well into adulthood. This puzzle is pure evil, I tell you. I don't even know why I'm posting it--I guess I must have an evil streak. It's the kind of puzzle whose author probably deserves to have his hand cut off. Well, I guess it's not that evil, since no communication tricks are involved.
Oh man, speaking of the -gry puzzle, that one's even worse. Supposedly, it first appeared on a radio show, and it got repeated everywhere, only when people repeated it, the words got mixed up in a way such that it was unsolvable. Um, yeah... these are the sort of stories you pick up when you're a puzzle enthusiast.
Anyways, it's actually a pretty easy puzzle. See the solution here in the comments.