Wendy Oldbag attempts this on occasion in Phoenix Wright: Ace Attorney. She's in her seventies, so it's not exactly successful. Its chief effect is to cause the most common target, Miles Edgeworth, to lose his composure and demand that it stop.
Larry Butz also has them when doing his Ocular Gushers bit. It virtually never works.
Phoenix Wright is said to have them too. Particularly effective when getting information out of the soft-hearted detective Gumshoe.
Dahlia Hawthorne does this, and it does tend to work until her true nature is revealed.
Her ex-boyfriend, Terry Fawles, does this in the courtroom lobby.
There's a humorous subversion in Mana Khemia Alchemists Of Alrevis. In one of Pamela's Character Quests, she enjoys making medicine that are actually dangerous to anyone who drinks it. Problem is, all the victims (even ROXIS!), although they know of the med's effects, cannot refuse Pamela's offer to test them, because of Pamela's Moe Moe eyes.
Maybe they should have tried it against the darkspawn horde...
Oddly enough, in Dragon Age II, Fenris of all people has a tendency towards this now and again, at least on a Hawke who's his friend; Merrill even namechecks the trope in a bit of party banter if Fenris is Hawke's love interest. It's remarkably effective, too...
Merrill would know. She's a master of this herself.
Mylune, a quest giver in World of Warcraft, says that she'll "give you the big eyes" if you don't save the fawns trapped in a burning forest.
Emi in Katawa Shoujo is rather good at this. Even when Lilly has hardened Hisao, he still falls for it when Emi pulls it.
Ventus in Kingdom Hearts: Birth by Sleep proves he knows how to do these when he asks Terra and Aqua to kill him to prevent the X-blade from being formed.
At one point in Little Busters!, Komari and Kurugaya are fighting over what nickname Kurugaya should have. She claims that even if Komari calls her Yui-chan she'll just ignore her, and demonstrates. In response, Komari gives such a sad, tearful look that Kurugaya takes a significant amount of damage.
Clementine from The Walking Dead has the option of breaking these out to win over any survivor of the player's choice in season 2. Even when she's not intentionally doing it, she's still adorable as can be.◊