In Japan, the yokai Tesso ("The Iron Rat") is a rat demon the size of a grown man, with iron teeth and claws. The story of Tesso comes from the Heike Monogatari, (referred to as ‘Japan’s Odyssey’), an epic poem from the Heian period that mythologises the Heike/Taira wars that split Japan as two factions struggled for the throne.
The Emperor asked if there was any other favour he could grant, but Raigo was adamant. So reluctantly the Emperor broke his promise. Outraged, Raigo went on a hunger strike and died after 100 days, cursing the Emperor with his final breath. At the time of his death, a figure in white appeared beside the cradle of the 4-year old Prince Taruhito, who died of unexplained illness soon afterward.
This is of course just one of multiple versions of the tale, coming as it does an oral storytelling tradition. Raigo was given the nickname Tesso by artist Toriyama Sekien in his yokai collection Gazu Hyakki Yako
In Western literature, HG Well's apocalyptic novel The Food of the Gods, features giant rats about the size of wolves.
And, lest we forget, there is Lovecraft's Brown Jenkin of the Dreams of the Witch-House; the titular witch's familiar with body of a large rat and the face of a man.