Please be aware that the award year refers to the Award Season the Annie Awards ceremony was held and not the year the film was released. So the 2002 Annies would be in connection with the Oscar ceremony held in 2002.
Most nominated film
2005: The Incredibles (16 nominations – 10 awards)
2006: Wallace & Gromit: The Curse of the Were-Rabbit (16 nominations – 10 awards)
2009: Kung Fu Panda (16 nominations – 10 awards)
2011: How to Train Your Dragon (15 nominations – 10 awards)
2016: Inside Out (14 nominations – 10 awards)
Most winning film
2018: Coco (11 awards – 13 nominations)
2005: The Incredibles (10 awards – 16 nominations)
2006: Wallace & Gromit: The Curse of the Were-Rabbit (10 awards – 16 nominations)
2009: Kung Fu Panda (10 awards – 16 nominations)
2011: How to Train Your Dragon (10 awards – 15 nominations)
2016: Inside Out (10 awards – 14 nominations)
2008: Ratatouille (10 awards – 13 nominations)