If you're clever you can contrive many sorts of situations in which it's advantageous to fail a skill roll, rather than succeed at it. Being mind-controlled (as in the comic), or coerced can make you attempt something you'd rather not do successfully.

But the best example of this sort of thing comes from the roleplaying game Toon, which is based on classic Looney Tunes style cartoons. In this game, if you find yourself suspended in mid-air over a perilous drop, you need to make a Smarts roll to realise that gravity should make you fall. If you fail, you're too stupid to fall.

Transcript

Kermit: Going on here, what is?
Chewbacca: I'm jamming the coded dance signal with a counter-dance.
Gonzo: Too late! I'm transmitting it!
GM: Sally, save versus Mind Control.
C-3PO: 8.
GM: You're compelled to dance too.
C-3PO: Okay. Dancing requires a skill roll, right?
GM: Well, techni—
C-3PO: Although I'm fluent in six million forms of communication, interpretive dance is not one of them. My Dance skill is -3.
Chewbacca: Good! You need to fail! If you do the dance properly, the sleeper agents will get the activation signal!
R2-D2: Natural 1! Natural 1!
[SFX]: 20!
{3PO dances}
C-3PO: On the bright side, six million and one.