It may well be that modern humans are the only animals whose basic activity levels are insufficient to maintain practical standards of fitness and health, and the only ones, perhaps, to exercise for the sake of getting fitter. But no one knows for certain.
Ducks, sparrows, crocodiles, salmon and lizards have all been shown to become physically fitter following laboratory training regimes. In the wild, fitness levels vary.
Some animals can maintain their form even after lengthy periods of inactivity; polar bears, for instance, retain body strength during months of hibernation.
Others lose it easily: king penguins, for example, experience considerable muscle loss while on land for the breeding season and must bulk up quickly once they return to the water.
Intriguingly, wild rodents will use hamster wheels placed in their habitats. But this might have more to do with inquisitiveness than fitness.