Human Hummingbird

When an animated character gets frightened, excited or angry, she may flail her arms or legs around so fast that they are literally a blur. Sometimes it's a complete blur; other times, you will see the arms or legs, but in multiple vision.

This trope comes in a few simple variations:

A character doing a Wild Take flails her arms, sometimes jumping in the air and flailing her legs, too. Occasionally, this will cause her to hover like a helicopter — or a hummingbird.
A character who is running Too Fast to Stop will have this happen to his legs while his arms appear normal. Any Innocent Bystander who gets caught in his path may become A Twinkle in the Sky. This is similar to but distinct from Wheel-O-Feet.
A small character being held At Arm's Length may swing her arms this way in a futile effort to strike the taller character.

This is a typical behavior for a Genki Girl.

If it's just the character's arms that move, that's Kewpie Doll Surprise. Also see Rapid-Fire Fisticuffs/Spam Attack for an offensive, usually the non-comical, version.

Examples of Human Hummingbird include:

Anime and Manga

Sakura does this while attempting to whack Touya for being a jerk in the first episode of Cardcaptor Sakura.
Sana Kurata of Kodomo no Omocha (shown above) does this at least twice per episode.
Tomo does this in the first episode of Azumanga Daioh upon finding out she's late for class.
This happens in an episode of Tokyo Mew Mew where Ichigo does this with her legs...until she slips on a piece of broken crockery.
Done in an episode of Dragon Ball, where Goku pretends he has a technique that lets him have eight arms. The trick, of course, is that he's waving them up and down so fast the after-image makes it seem real. This is in response to Tienshihan's technique of actually growing a second pair of arms.
Negi of Mahou Sensei Negima tends to do this when the students mock or belittle him.
- Same with Becky of Pani Poni Dash!.
Done quite often in Slayers.
In Kurogane Pukapuka Tai, Commander Kuki does this when Captain Mary forcibly kisses her.
Subverted in Umineko no Naku Koro ni, Jessica tries this and gets interrupted by an asthma attack.
This happens to Yachiru frequently in Bleach.
The main character in Fruits Basket.
In the [[Sonic The Hedgehog: The Movie]], Knuckles reacts this way upon discovering, "My hat's on fire!".
This happens to many girls frequently in Fairy Tail, particularly when humorously distressed or angry. Lucy does this most often, and Coco from the most recent arc is guilty of this as well, running around the room and doing this as she talks to people.
Midori from Midori no Hibi, another Genki Girl.
Taiga, yet again a Genki Girl, does this sometimes in Fate/stay night, at least in the game. She doesn't move her arms that fast though since Fate/stay night doesn't really use cartoonish body movements like that but Taiga's antics does push it sometimes.
Brook from One Piece runs so fast that you see multiple legs. Especially when he runs across water.
Yui from Lucky Star often does this when she's waving to greet people.
Suzu of Amuri in Star Ocean flaps her arms on a regular basis and for no particular, to the point that she has to use her hair in place of hands.

Comic Books

Getafix does this in Asterix and the Big Fight, but that was mostly pointing while yelling orders.

Live Action TV

Vicki did this in the Small Wonder episode "Vicki and the Pusher".
El Chavo, whenever someonoe suggests him doing something exciting.

Video Games

Yoshi's Flutter Kick arguably does this.
- Chun Li's definitely does.
Extremly noticeable with Shiki in The World Ends With You. Her waving image lasts longer than most, due to the sprite-based nature of most cutscenes.
Early Sonic the Hedgehog games had Sonic's legs turn into a blur.

Web Comics

In El Goonish Shive, Grace does it here.

Western Animation

The Simpsons has two rather literal examples of this; in one Halloween Episode, Krusty's pacemaker shorts out and gets set to Hummingbird Mode ("Nectar! Nectar! Gotta drink my weight in nectar!"). In another, we see security cam footage of Apu thinking he's some kind of hummingbird after working for 96 hours straight; he tip-toes across the Qwik-E Mart, flapping his arms and humming (he also says that he tried to drink nectar out of Sanjay's head).

Real Life

It is possible to do it with the right lighting, such as CRT displays and other strobing light sources.