The titular doctor in Dr. Horrible's Sing-Along Blog at the beginning of act two. Oddly, he's not trying to garner sympathy. He's just crushed that he inadvertently introduced his archnemesis to the girl of his dreams. He also has the puppy-eyes after telling his viewers about the failure of his latest crime ("Captain Hammer... threw a car... at my head").
The Whateley Universe has Jade "Generator" Sinclair and Bunny "Bugs" Cormick. The former looks like a 11 year old girl (she's 14) and the latter, at first glance, appears to be your typical teenage blonde bimbo (when not in Mad Scientist mode). Both are both so good at this that their friends often joke that it's one of their mutant powers. Bugs even managed to win her combat final just by crying.
The Nostalgia Critic's pretty blue eyes have a tendency to go puppy-wide whenever he's suffering. This is particularly noticeable in Kickassia, where he stays like that for at least three scenes. (The ham-tastic conversation with Spoony, after he accidentally kills Santa Christ and when he's pinned to the fridge by the others.)
Doug's new character, Donnie Dupre from Demo Reel, knows how to manipulate his long-suffering male writer with them.
A live version of the page image appears here on Cute Overload.
Chakona Space features a mouse trying it on a coyote starship captain. It doesn't work quite as planned.
(Penny) gave Yote her best wide-eyed helpless waif look, which might have worked a lot better if she wasnt so well fed and sexy.
In The Blockbuster Buster's review of Shrek 2, the title card artist E-Joy pops in, much to the shock of Eric, who wonders who she is and asks for one reason why he shouldn't fire her. She invokes this trope and is able to stay, much to her delight.
Parodied in this lolcats picture. The cat has a solution to this situation: Just shut the door and don't look at the culprit. Nobody asked to see those sad eyes.
Gaea in the Noob webseries and comic, as one of her Manipulative Bastard tricks. A couple of her male guilmates have tried to imitate her, only to be told they look silly doing it (for the Butt-Monkey) or can't measure up to her (for the Manchild). One of her minions tried to pull them on her in the first movie.
This is Ellen Rose's most powerful strategy in Outside Xbox. For example, on the Show of the Weekend episode discussing the Kobolds and Catacombs expansion for Hearthstone: Heroes of Warcraft, Luke discusses the effect of King Togwaggle, who lets you hold the opponent's deck to ransom, by getting Ellen to go to the kitchen and then stealing her seat:
Luke: Ellen, I have stolen your place on the sofa, like the sneaky King Togwaggle. Ellen, what ransom will you give me to switch back? Ellen: Sad puppy eyes. Luke: ...Ugh, fine. I would have liked to hold out for more than two seconds.