Fruit flies, bees, and wasps that feed on naturally fermented saps or honey are often then unable to fly. Indian sloth bears become inebriated sucking on fermented flowers. Bohemian waxwings are often found dead after feeding on fermented rowan berries in Scandinavia. Post-mortems show that some even have liver disease. Elephants get drunk and dangerous, and can smell alcohol. In 1974, 150 Asian elephants broke into an illegal sill in west Bengal, drank the alcohol, and went on a rampage, killing 5 people and destroying many buildings. Cats and racoons are known to drink.
Studies with green vervet monkeys show that they respond to alcohol as humans do, most drink moderately, 15% drink heavily, and 5% are serious abuse binge drinkers who drink as much as they can, pick fights, and pass out.
Update:
In January of 2003, the waxwings were at it again, with thousands getting drunk on fermented rowanberries at Karlstad University in Sweden. According to University spokesman Hans Jensen,
So far some 50 drunk birds have lost their lives when crashing into the university's big windows. But the worst is over, the berries are beginning to run out.
In December in Sweden, police in a town called Karlskoga had to kill an intoxicated big-horned elk after it charged an 8-year-old boy; it had gotten drunk by munching on fallen apples that had fermented on the ground.
Sources:
CNN.com, January 15, 2003
Sunday Telegraph, 3 March 2002