From Scientific American:
Remember how one becomes a zombie in the first place? Through death, or Intercision, or, since this is a science blog and we need to explain this scientifically, through the effects of tetrodotoxin. In any case, the process incurs some permanent brain damage.
One of the brain centers that is thus permanently damaged is the circadian clock. But importantly, it is not just not ticking any more, it is in a permanent "day" state. What does that mean practically?
When the clock is in its "day" phase, it is very difficult to fall asleep. Thus insomnia.
When the clock is in its "day" phase, metabolism is high (higher than at night), thus zombies require a lot of energy all the time and quickly burn through all of it. Thus constant hunger for high-calory foods, like brains.
Insomnia, in turn, affects some hormones, like ghrelin and leptin, which control appetite. If you have a sleepless night or chronic insomnia, you also tend to eat more at night.
But at night the digestive function is high. As zombies' clock is in the day state, their digestion is not as efficient. They have huge appetite, they eat a lot, but they do not digest it well, and what they digest they immediately burn. Which explains why they tend not to get fat, while living humans with insomnia do.
Finally, they have problems with wounds, you may have noticed. Healing of wounds requires growth hormone. But growth hormone is secreted only during sleep (actually, during slow sleep phases) and is likewise affected by ghrelin.
In short, a lot of the zombies' physiology and behavior can be traced back to their loss of circadian function and having their clock being in a permanent "day" state.
Although, it is not true that insomniacs must therefore be zombies, i'd say we should all be wary just in case (i'm looking at you, fnord12).
(Ha! A zombie post filed under Science.)