Do you think animals pollinate flowers and disperse seeds on purpose or by accident?

Animals most likely pollinate by accident.

Explanation:

Deer for example, they may graze in the grass. The pollen/seeds could catch onto their fur--and later fall off into a different area when they walk away. They could also eat a plant, and the seeds end up in their feces. Bees for another example don't necessarily mean to pollinate, they just happen to pick up pollen/seeds when they land on a flower for honey.

Hope this helps :)