This is purely anecdotal, but from my experience the following are most common in US Zoos, and the species I have seen in the most zoos:
1. Laughing Kookaburra- since I started my lifelist, I have seen this species in more Zoos than any other species, in the majority of AZA Zoos and plenty of other facilities as well.
2. North American River Otter- tied with the Kookaburra for species I've seen the most. Not very common in non-AZA Zoos, but definitely common in the AZA- and I've seen these at substantially more Zoos than the Asian Small-clawed Otter, though this might be a regional thing.
3. Sulcata/African Spurred Tortoise- a lot of Zoos hold this species, both AZA and non-AZA. The reptile species I have seen the most often, with most individuals being surrendered pets/rescues.
4. Two-toed Sloths- if the two species are lumped together, I would have seen this animal at more Zoos than the Kookaburra and otter, as almost everywhere has a sloth on exhibit.
5. Emus- seen at a lot of zoos.
6. Red Kangaroos- presumably one of the easiest, and cheapest, popular species to manage. They don't require an unreasonable amount of space, and are common even outside the AZA.
7. Scarlet Ibises- Kept by a lot of AZA Zoos, primarily in large free-flight aviaries.
8. North American Porcupines- small, easy to keep species that can be kept outside year-round, plus generally considered cute makes this an appealing option for Zoos.
9. Ring-tailed Lemurs- easily the most common primate in US Zoos, kept by many Zoos both AZA and non-AZA Zoos.
10. Harbor Seals- I'd expect this one to be less common in other parts of the country, but many Zoos and Aquariums around here keep this species.
11. African Lion- obviously a popular species, and one that many Zoos want to keep if able. I've seen this animal at more Zoos than tigers, though not sure if this is universally the case.
12. Giraffe- both masai and generic giraffes seen at many Zoos, both AZA and non-AZA.