Mordor's giant cows are no match for Boromir's forearms.
"He stood in the center of the room, his head thrown back in silent laughter, his arms raised above his head, his fists clenched in that famous, overly dramatic gesture known to theatre students everywhere as 'milking the giant cow'. Yes, it was hokey and clichéd, and Voltmeter knew it, but he loved doing that gesture anyway, the quintessential stance of a man mad with power."
Tengen Toppa Gurren Lagann: Kamina makes a frequent habit of waving his arms wildly when delivering his bombastic speeches (aside from his heaven-bound dramatic pointing), whether in a mecha or not, even disregarding that he's in the middle of a heated battle, completely ignoring the enemy's presence, much to the annoyance of everyone (save Simon, Nia, or Kittan).
Duke Red often does this while monologuing about his various mad science schemes in various Osamu Tezuka productions, especially Metropolis. It's actually rather effective there, since he's supposed to be completely unhinged.
Code Geass: Lelouch Lamperouge, being a Large Ham, does it all the time. Even when simply removing a contact lens, which coincidentially unlocks his Geass power, but that's details. At some point, C.C. asks him why he needs to be so theatrical when he uses his Geass, and he tells her to shut up.
It should be obvious to C.C. and the audience; if he's only exposing his eye during the instant of one command, a flourish would draw the required attention to that eye.
Doc Brown of Back to the Future wildly gesticulates whenever he speaks. In the Making Of, director Robert Zimeckis said Christopher Lloyd was taking inspiration from the conductor in Fantasia, and described him as 'conducting the world'.
Rome The Forum newsreader played by Ian McNeice punctuates his hammy news bulletins with stylized gestures and poses that were actually used by professional speakers and politicians at the time. At one point Lucius Vorenus tries to use them during his brief attempt at politics, but completely fails to make them seem impressive.
Baron Vladimir Harkonnen of the Dune mini-series, also played by Ian McNeice. Just watch this
Along with his oddly placed vocal pauses and emphasis on unusual syllables, this is a key element to the William Shatner acting style, famously perfected as Captain Kirk on Star Trek: The Original Series. Indeed, one filk song ("Star Trek Rhapsody") even name-checks it:
This was quite common on The Original Series in general. Many of the actors were originally trained for the stage, where overemphasised actions were expected; on screen, this translated to hokey action scenes and sometimes hilariously overdone body language.
Angel. Wesley does this while spoofing the Buffy/Angel romance in "Fredless".
"Oh Buffy, I love you so much I almost forgot to brood!"
The video for Disturbed's Indestructible uses this several times. Hell, every Disturbed video contains a little of this, as do the live shows. The singer is one great big ham.
The director for the Music Video to Elton John's song "I Want Love" accused Robert Downey, Jr. of doing just this. Her solution? Taping his hands in his pockets to remind him that understatement worked more for this concept (the idea was just Downey walking and lip-synching to the song in a cold 'institutional' building). Works, too.
Kevin Hart mocked R&B singers' tendencies to do this when giving "tips" on how to be a singer:
Kevin: All you need to know how to do is open your hands, close em, and point.
Microsoft 3D Movie Maker: Because of the fairly cartoonish style, many of the actions are Milking the Giant Cow. The limitations of the graphics technology at the time play a part in this too. For instance, since there was no way to animate a person convincingly speaking over recorded dialogue, the action for talking was for the characters to lean forward, nod their heads, and wave their arms around.
This speech is spoken by Barrymore in the play I Hate Hamlet
In the Reduced Shakespeare Company play The Complete History of America (abridged), Reed tries to mime steering a car, but his gestures are off enough that Austin tells him, "Stop milking that cow!"
In Andrew Lloyd Webber's The Phantom of the Opera, depending on the actor (although this is usually done by the actors) Erik (The Phantom) does this so often he could be considered the Giant Cow Dairy Farmer.
Subtly lampshaded in RENT; when Maureen is doing her protest, she raises her arms dramatically—but she's actually milking a cow when she does it.
And I lowered myself beneath her giant udder... and sucked the sweetest milk I have ever tasted.
In tradition Japanese noh theatre the main (usually) actor will pause in exaggeration pose for dramatic effect.
Justified trope for games that use a Super-Deformed art style—since the character's face is often just a very tiny rectangle with even tinier dots for eyes, extremely exaggerated body language is necessary to get the emotion across. Even motion capture has not escaped this trope. Given the limits of technology, it's not (yet) possible for mo-cap to pick up subtle gestures and facial expressions, so many actors are encouraged to unleash their inner Large Ham.
Especially true in early-90s Adventure Games of the point-and-click variety. The graphics were just advanced enough to animate body movements to go along with the Mouth Flaps, which can get tiresome when the player had the option of full audio in games like Gabriel Knight, since the wild gesturing (on a loop) was a lot less noticeable in the time it takes to simply read the dialogue on-screen.
Monkey Island Stan the Salesman and its sequels parodies this by flailing his arms wildly no matter what he's saying. It also serves to draw attention to his Unmoving Plaid jacket, making it even more amusing.
In Ape Escape 3, Specter and Dr. Tomoki have a tendency to do this in FMV cutscenes, making them look like mad puppets.
Xehanort from Kingdom Hearts tends over-exaggerate with his hands throughout the series, but his latest (or earliest?) incarnation as Birth by Sleep's Master Xehanort takes milking the giant cow (ofdarkness!) to a fine art. The man is seemingly unable to make speeches without making clutching/grasping motions of some sort.
Justified with his Nobody counterpart, Xemnas, As Nobodys have no hearts they also have no emotion therefore have to exaggerate their feelings.
Kingdom Hearts 3 D reveals their bodies can simply create a replacement heart with time, implying he might just be doing it for the heck of it.
In the in-game cutscenes in Heroes Of Might And Magic V, the characters have a very small pool of body language expressions, almost all of which are highly overblown and Hammy.
In Castlevania: Lords of Shadow, the Lord of the Necromancers spends five minutes pacing around Gabriel and communicating entirely through his hands during his Motive Rant, possibly because his face isn't visible.
In Silent Hill 3, Vincent is never able to keep his hands still while talking.
The animation for the "Rally" combat action in Dragon Age: Origins is this; Loghain, already a Large Ham, is particularly fond of this action. In the sequel, loose cannon party member Anders does this while casting Firestorm, accompanied with "MY MAGIC WILL DESTROY YOU!" or wordless screams of rage for maximum ham potential.
Dark Souls has an emote that does this called "Praise the Sun" where you raise you arms above you head in a "V" shape. This emote is exclusive to members of the Warriors of Sunlight.
After The War: both Dr. Z and Holeman seems to do this a lot. They're both hams after all.
Characters in 8-Bit Theater do this occasionally to represent despair, surprise, or just to emphasize a point. Of course, it's because 8-Bit Theater is a Sprite Comic of an 8-bit game, and thus has few sprites to express any emotion. Occasionally, it's lampshaded. ("Put your hands down!")
Daffy Duck in the Great Piggybank Robbery and other Looney Tunes.
Hexadecimal in Re Boot very often, though it's justified: her mask changes off-screen with every swipe of her hand.
Avatar The Last Airbender: Katara, while mocking Sokka for his big ears, decides it is necessary to mime "elephant ears" using her hands, along with pointing dramatically as if she has an objection. Apparently this is a genetic trait: later, in season two, Sokka gets a little...intense while cheering and booing during the earthbending tournament.
MMA fighter Anderson Silva has a tendency to do this at extremely emotional moments.
When the terms of the Arab Maghreb Union (a common market treaty between Mauritania, Morocco, Tunisia, Algeria and Libya) were being read out, Muammar Gaddafistarted waving his fists in the air with a smile (he was known for having been particularly obsessed with a Pan-Arabian/Pan-African union).
Valdis Pels, the host to the popular Russian game show Ugadai Melodiyu (Guess the Melody) is known for waving his hands around whenever a song was playing. Russian comedians loved to poke fun at him for that. One joke involves a cop trying to unsuccessfuly trying to handcuff him while a song is playing.