Joachim from Shadow Hearts Covenant always had some wacky weapons, such as a red mailbox, a giant, frozen Tuna, a desk and literally THE Nautilus, somehow shrunken, so he can hold it while striking wrestling poses.
Come to think of it that game had some other bizarre weapons. Anastasia fights with fabergê eggs exclusively, including one from space and Gepetto uses his Lolita puppet to fight. That game was really something else, read japanese.
On that note guilty Gear comes to mind. I-No was a witch that wielded an electric guitar, Venom fought with a queue and billard balls, Milia used her hair and Bridget attacked with jo-jos. I have a feeling that most things listed here will come from japanese games, unconventional stuff seems much more common there. So to give western developers at least some representation i will mention one of my favourite game series Ratchet & Clank. From the vast amount of interesting weapons to find in this series i want to only mention one: the rift inducer, a gun that shoots black holes for your enemies to be consumed by. Watching several goons walk to close to your placed portal and listening to their screams as they're dragged into the nothingness was a treat hard to replicate with any other weapon. It was the gun that, for me, made a merely good game great.