Dante and Vergil's amulets in Devil May Cry, which also serves as one of the keys to the gateway to Hell; in the original game, Dante discovers that Nelo Angelo is Vergil after he (Nelo Angelo) explodes, leaving behind Vergil's amulet.
In Kingdom Hearts, at the beginning of the first game, Kairi talks about a lucky charm she's making from seashells. Later in the game after Sora rescues her from Hollow Bastion, she gives the finished charm to Sora as a memento. However, the Oathkeeper is a little different from your typical Memento MacGuffin in that it also has a practical purpose; it's one of Sora's best weapons throughout the series.
He also makes a promise when he gets it to give it back to her, about 3/4 of the way through the first game. At the end of Kingdom Hearts 2, when he does manage to return home despite all odds, the first thing he does is give it back.
The Clefairy doll from the Pokémon series. Your hero buys a doll in generation one and gives it to Copycat in exchange for some random TM. The next generation, three years later, has her freak when she can't find her special doll, so you have to go find it.
The Memento Ring in Final Fantasy VI is the source of many Epileptic Trees. It's described as a memento of Relm's family. So naturally, Relm can equip it. Except Shadow can too. Other in-game cutscenes make it pretty clear that, yes, Shadow is Relm's father... so why the hell can Gogo equip it?
Perhaps s/he mimics being a member of Relm's family? Or maybe s/he's some long-lost relative?
In Final Fantasy VII, Aerith's materia was given to her by her biological mother and she keeps it as a memento, unaware that it is in fact the extremely important White Materia.
The pendant from Chrono Trigger goes through several stages as a memento, aside from literally being a MacGuffin. At first it's just a family heirloom belonging to Marle, but Crono holds onto it after she disappears and continues to do so when she's rescued. Later, after Crono's (temporary) death, Marle takes it back as a memento from Crono. Interestingly, Magus never seems to think of it as its original status as a memento of Schala.
In The Longest Journey, April receives a stopped watch from Brian Westhouse, who claims to have received it from the Cool Old Guy Cortez and that it represents "Cortez's heart". After she rewinds it, it helps her get back to her world. Much later, when it seems like Cortez dies, the watch stops again.
Link gets a fishing pole very early in The Legend of Zelda: Twilight Princess. It seems like it's nothing more than a gesture of affection from Colin, whom he treats like his adopted little brother, but it comes in handy more than once during the plot. It can even be used to distract the Big Bad during the final battle, in keeping with Zelda tradition.
The Fairy Ocarina that Saria gives Link when he leaves the Kokiri Forest in The Legend of Zelda: Ocarina of Time could count as one too, since it's an important item for plot-advancing (you can't open Dodongo's Cavern if you don't learn Saria's Song, for example), but this is a downplayed example because, once Link retrieves the titular artifact, it replaces the Fairy Ocarina in the inventory for the rest of the game.
In Persona 3 and Persona 4 when maxing out a social link you receive an item of some importance to the character you maxed out the link with. It's needed in order to prove to Igor that you can fuse the strongest Persona for the arcana of the link in question.
Alpha Protocol: Sis's locket is a childhood memento. If you spare her after the boss fight, she gives it to you, symbolically letting go of her childhood, which wasn't a bed of roses...
Sir Francis Drake's ring in Uncharted 3: Drake's Deception, subverted twice, the first time it's seemingly stolen, it turns out that it was a fake and Nate still has it with him. They're using it simply to lure the bad guys out since they are treating it as a MacGuffin. The second time, when he actually does lose it, Nate is shown to care more about rescuing Sully than getting it back.
Final Fantasy Tactics: The "reed flute" is more of a skill (the ability to turn a leaf or blade of grass into an instrument) than an actual momento, but it's something that binds Ramza and Delita both to each other and happier days. (Ramza also bonds with Princess Ovelia when she reveals that Alma had taught it to her.)
A picture taken in the final route of Duel Savior Destiny that shows the bonds between the main cast becomes an extremely helpful tool for everyone that allows them to surpass their former limits through The Power of Friendship.
In Resident Evil 2, Sherry Birkin carries a locket with a photo of her and her parents. Behind the photo is a vial of the G-Virus, which the Umbrella Corporation has by this time killed a city trying to obtain.
In Dragon Age: Origins, Alistair remarks that he wishes he had something belonging to Duncan, the deceased leader of the Grey Wardens in Ferelden, whom he had viewed as a father figure. The player character later has the opportunity to retrieve Duncan's shield from a hidden warehouse and present it to Alistair, who treasures it. The game even equips it onto him automatically.
In the City Elf origin story, a female Warden may elect to keep her wedding ring, if she loots it off the body of her murdered betrothed, in memory of him.
In the Human Noble origin story, the Warden may choose to keep and wield the ancestral sword and shield of the Cousland family, almost all of the other members of which have been murdered.
A Dalish Warden will be presented with a token of remembrance by the Keeper of their clan before they leave with Duncan to join the order.
A Warden of any background will be presented, during the Gauntlet at the Temple of Sacred Ashes, with a talisman called Memento. It's given by the ghostly image of someone dear whom they lost during their origin story, and is specifically intended to invoke this trope.
In Planescape: Torment it's possible to find the wedding ring from a previous incarnation's lover, which she specifically left for you. It grants some good defensive bonuses and, if kept throughout the game, can be upgraded to become one of the more powerful rings in the game.