Several mammal species are adaptable enough to withstand any changes made to the world. But these animals are regarded by humans to be nothing but mere pests. However once humans are gone, these animals will reign supreme.
When will it all happen? No one knows. There are theories though. How will it happen? Could be the same thing that killed the dinosaurs. However, humanity it's self might be our own undoing. Humans are smart, maybe too smart for their own good. We pollute the Earth with toxic materials, we chop down forests at the rate of acres per minute, we have ruined the ozone with hair sprays and other chemicals commonly used in our homes, and the list goes on. We have built on every piece of land the World has to offer, including the oceans. All this expansion and technology will most likely be the thing that kills us. The things that will live past us are the more adaptable little creatures, or animals that know how to make the best out of a bad situation.
When mammals change, they do it in a big way. Pay no attention to Animal Planet's "The Future is Wild", squids will NEVER take over the World. Maybe the waters, but never the land. Gravity would surely play against them. And if history is any indication, major animal groups do not die off. We still have reptiles left over from before the dinosaurs. The dinosaurs are believed to have become the birds of today, and mammals will always be around as well. If humans do manage to get away, well, where would they go? No other planet that we know of yet is like Earth. Nothing can survive elsewhere and people have already attempted and failed to live inside an artificial environment. So what else is there?
Humans can only accept their fate gracefully the way the dinosaurs did and many other creatures before us. We can also hope the World will regenerate and change back to the world it once was.