Yeah, runaway global warming might not happen. Plant monocultures would begin to disappear. New invasive species wouldn’t happen, though existing ones might have a better time for a bit. Major thoroughfares wouldn’t create barriers to migration. Dams might take centuries to collapse, but I think humans going extinct might have one of the biggest impacts.
But if you exclude humans, that's where you have some debate. I see bees and spiders mentioned in this thread and I'm inclined to agree with bees, because of how vital those dudes are for pollination and thus for any animal that ultimately relies on plants (hint: that's all of them! predators also need a population of herbivores to feast on)
Ever wondered what happened to all these bugs on the car when driving through the countryside? There is already something big happening and we are just getting started.
Here is a talk on the topic of insects driven to the point of extinction due to neonicotinoid pesticides (unfortunately the talk is in german. Maybe someone is able to find a english version)
https://www.youtube.com/watch?v=Z_p9yYXZuCI
Bees and coral are both great answers, but I’m going to go with spiders. The amount of smaller pest insects that spiders consume is definitely overlooked and without them just imagine the swarms of bugs that would aggregate during the summer months