At Roger Williams Park Zoo, I saw the old Tropical America exhibit on a number of occasions, including the adjacent Conservation Corner back when they actually exhibited burying beetles! I also as a child really enjoyed the Australasia exhibit, which has since been renamed to "World of Adaptations" and displays more of a hodgepodge of species. Back then, the exhibit had parma wallabies, chinese alligators, archerfish, a walk-through aviary, tree shrews, and a number of small herps that are no longer part of the collection. Across from Australasia/next to Tropical America was a kangaroo exhibit that was demolished when Faces of the Rainforest was built. Only in this past year, the old Aoudad exhibit has also been demolished, in order to make way for a new Education Center, which is sorely needed. I'll still miss that exhibit, however, as it was one of my favorite parts of the zoo, especially back when they had a larger herd of aoudads.
At Buttonwood Park Zoo, I remember the old Aquatics Building prior to it being replaced with Rainforests, Rivers, and Reefs. I don't miss that one too much, however I regret not appreciating the shorebirds as much when they were there. At Capron Park Zoo, not many exhibits have left in my lifetime, however there were two small, standalone exhibits that got demolished in recent years- one which most recently held Southern Screamers, and the other Golden Lion Tamarins. For other local zoos, I don't really remember any exhibits closing during my lifetime, although I can recall some that changed significantly (e.g. Stone Zoo's old Flamingo exhibit was renovated for African Spurred Tortoises).
On a more national scale, my 2016 visit to Cleveland Metroparks Zoo I remember seeing Monkey Island.