Since rotary fans essentially "chop up" air as part of its function, speaking or breathing into a fan will cause a distortion effect on the voice.
Even if it's a recent production, anime and manga use the wire-cage-&-clear-blue-blade fans that haven't been sold in the US since the 1990's (small fans nowadays will typically have a plastic cage instead of steel; wire-cage fans are still sold, but they're likely to be the large commercial variety). These fans are increasingly rare in Japan, too, but since most manga authors grew up in the '90s or earlier, they're still present in their works.
Note that you can achieve a similar vocal effect with a modern plastic fan. The old wire-frame ones are somehow more satisfying, though.
- In an M&Ms ad announcing the return of Crispy M&Ms, Yellow does this by accident. (He'd misunderstood what Red meant by "tell our fans".)
- A radio ad for Geico motorcycle insurance has a woman sitting close to a fan in her office because she misses the feel of the open road on her cycle; all her dialogue has that sound.
- Lucky Star: Konata and Tsukasa do it. Kagami calls them out on it, but Kagami's father mentions that she does the same.
- In the manga, the question of whether or not Kagami does it never comes up; she says Tsukasa was doing it earlier, and that's the end of that.
- Also happens in Hidamari Sketch, where Yuno and Miyako catch Sae talking into the fan, pretending to be an alien.
- Azumanga Daioh: Osaka does this while riding with Nyamo to Chiyo-chan's summer home.
- Pictured above, Kaguya Houraisan in the official Touhou yonkoma strip Inaba of the Moon and Inaba of the Earth. If you're wondering about the bunnygirl's reaction, they're from the Moon.
- Ritsu in Season 2 episode 11 of K-On!.
- Komori in Sayonara, Zetsubou-Sensei, explaining what she would do on days of privation.
- Nozomi does it in Mayoi Neko Overrun!. "Nya-a-a-a-a-a-a-a..."
- Yukito does this in an early episode of AIR.
- Bobobo-bo Bo-bobo once got second place in a contest for doing this.
- The iDOLM@STER: Hibiki does this once before the Beach Episode.
- Thermae Romae: After being transported to modern-day Japan, Lucius finds himself inexplicably compelled to do this.
- Nichijou: Yuuko is tempted into doing this, but cannot due to a label prohibiting it.
- Tommy Boy: Luke... I am your father!
- Done by a giant, dementia-suffering grandfather in Big Man Japan... with an airplane's propeller.
- Rizzo and Pepe do this in Muppets from Space as part of a scheme to get Gonzo to build them a Jacuzzi.
- Shriek If You Know What I Did Last Friday the 13th: The Killer spoke through a fan to mimic Ghostface's voice modulator. Dawson and Martina find the fan when they search him (it's one of those end-table models that really has no hope of being portable).
- Everybody Hates Chris: Chris's father is so cheap that he even complains about how much electricity this stupid fan game uses.
- MythBusters showed a similar effect during the episode "Brown Note" when Adam stood in front of low-frequency speakers. Adam being Adam, he naturally took advantage.
- This is how the vocal effect on "I... AM... IRON MAN!" was achieved.
- This fan video features Fluttershy from My Little Pony: Friendship Is Magic saying "Yay" into a fan.
- Martha Speaks: Martha and TD do this at the start of "Martha Spins a Tale." Helen finds it irritating.