No, they're quite rare, but there's a lot of versatility in what someone has or not. My world has billions of people, so even if there are thousands of devil fruits, that's still rare.

Zoans are given an extra animal species: like dogs, cats, koala, leopard whatever, logia are elements like smoke, fire, sand, magma, light, and paramecia is even more "anything." Rubber, earthquakes, iron cuffs, duplicating body parts; things like that.