All the time. On my normal rides I see deer, cows, sheep, goats, dogs, coyotes, rabbits, many kinds of birds, suicidal squirrels & field mice.
From various rides:
Chickens and pig near Santa Cruz
Peacock in Pescadero
Sheep in Pescadero
Ducks in Ireland
Deer in Calgary
Cow in Pescadero
Cows in the Netherlands
Monkey in Singapore
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Countries I've ridden in: US, Canada, Ireland, UK, Germany, Netherlands, France, China, Singapore, Malaysia
States I've ridden in: Illinois, Connecticut, Massachusetts, Pennsylvania, California, Nevada, Missouri, Colorado