Separation anxiety disorder occurs in many mammals in the animal kingdom, including humans, dogs, and cats. In humans, it is most common among children, especially in the earliest stages of life as they develop their emotions through experience. Babies become attached to their mothers and other family members (and even play objects) and associate them with a feeling of comfort and familiarity. When the person or object is taken away, anxiety ensues. In children, this makes perfect sense, as they are essentially helpless when abandoned. The disorder becomes a problem if it continues on throughout life, and may lead to (or be a result of) a deeper obsessive-compulsive or co-dependency issue.
In pets, separation anxiety can lead to obsessive behaviors such as constant barking / meowing, digging, or destruction of household objects. Some animals are more dependent than others, unable to spend hours apart from their owners. Among animals, the disorder can even be contagious; a normally non-anxious animal can adopt the behaviors of another animal, given sufficient exposure, or the symptoms may be alleviated. There really is no way to predict whether interaction with another animal will help, but if the owner is present during "play time," the symptoms can be kept in check and are less likely to affect the "normal" animal. The best way to treat animals who suffer from the disorder is to slowly wean them off of their dependency, as they are mentally convinced each time their owner leaves that they may never see them again. The solution is to gradually leave for longer and longer periods of time, constantly reassuring the animal that you will be back. The animal must be given plenty of affection whenever possible, as dependent pets tend to be more emotionally needy on all levels.
I have substantial experience with the disorder, as I am profoundly in love with my girlfriend and have had to live without her for extended periods of time on a few occasions (generally less than a month). I have been an on-off smoker for several years, and find it perfectly easy to quit entirely in the presence of my girlfriend. As soon as she's out of town, I become gloomy and constantly obsess over worst-case scenarios (like a plane crash, car accident, rape, mugging, murder). I feel that if she's away from me, she isn't safe, and that there is no way to know if we'll ever be together again until the moment I see her in person. If I don't hear from her within sufficient time on the phone, it gets even worse, leading to increased irritability and a general sense of "illness," accompanied by symptoms similar to a cold. I resume smoking cigarettes, drink more often than usual, and mope around constantly trying to distract myself from my thoughts (E2 and work help dramatically). I absolutely cannot stand sleeping on our queen-sized bed by myself. I wouldn't be surprised to discover that separation anxiety is just another manifestation of obsessive-compulsive disorder, as I find them difficult to separate. The tendency towards rumination (often negative) seems to drive the disorder, which makes me wonder exactly how sentient our furry companions are.
My girlfriend is somewhat of the same way...this last time she had to go, she got a cold immediately. Like me, she is somewhat of an emotional person, although far more expressive than I. As luck would have it, we managed to adopt an extremely emotional cat as well. His obsession is meowing and occasionally, biting. He only seems to do it in the presence of humans, however. When I get home after leaving him home for an entire workday, he "chews me out" with a constant barrage of needy "meows." He jumps on my lap, licks my face, and continues to emit the most pathetic, drawn out, saddened cries for attention. As soon as my girlfriend left, he began to exhibit these symptoms. When she calls me, I can hold the phone up to his ear and he will meow endlessly. When people walk by our apartment, he cries out for their attention. There's very little I can do other than provide him as much affection as possible, since I have no choice but to go to work every day. Pets quickly become familiar with their owner's departure routine, associating the jingling of keys or the sound of the shower with the inevitable absense of their beloved caretaker. One would do well to dole out affection whenever possible during this routine, to reassure the pet as much as possible.