It's not so much the global warming itself that results in negative consequences for life on Earth, but rather the Climate Change that comes about because of it. We don't fully understand the complete impact over time, and it will vary based on how much the temperature warms in the next 50 years, but some of what is predicted is a change in precipitation patterns - extended drought or extended rain/snowfall in places where that is unusual. Stronger hurricanes and cyclones as they feed on the warm water.
The biggest potential effect will be with animal, plant and insect species, as the climate may change too quickly for many of them to adapt, thus leading to their extinction. Since we don't fully understand the food chains, some of these animals will disrupt our food supply as well. The honeybee is a good example of a species that is already struggling, and we rely on it to pollinate many of our food crops.
Some rather obvious evidence of global warming taking place is the rapid disappearance and shrinking of glaciers around the globe.