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.
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.
This seems to be Pamela's, er... weapon throughout Atelier Series. A far less dangerous example occurs in Atelier Iris 3, involving the quest for decorating the Grimoire Castle's library.
In Banjo-Kazooie: Nuts and Bolts, the titular pair does this in an attempt to have the Lord of Games give them their old powers from previous games back...it fails.
He winds up giving them back in the end, however, in case Nuts & Bolts didn't sell well. Not surprisingly, it did, lampshaded by Mumbo in game no less.
Mumbo: Need to put floaters on boat, otherwise, boat sink like this game at retail.
Your Mabari war hound in Dragon Age: Origins can do this to anyone. It even works on Morrigan.
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.
Max tries to pull this off in "Abe Lincoln Must Die!" to get into the War Room, but fails.
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.
