My list isn't very extensive, but then again, I'm not dedicating travels to visit zoos like many in here:
Actual zoos, bird parks, terraria and aquaria: 48
Other places with animals (amusement parks with a few exotic animals, farms, butterfly farms, natural history museums exhibiting living animals, falconaries and the sorts): 14. If ANY place with animals counts, then probably several more, as I haven't been able to count any museum with a few terraria and aquaria or city parks with a few aviaries with birds like peafowl and pheasants.
So all in all, that makes at least 62, but I only really consider the 48 of them as actual visits. Hitting the 50-mark this summer, by the way.
That number was actually quite higher than I thought. On the other hand, most zoos/aquariums I've visited have been some Danish ones, and Danish zoos are generally very small - in either area or collection (there is NO Danish zoo with more than 100 species that has an area at more than 11 hectares) and usually also in significance. So I've only seen a very few of the big players in the zoo world.