Flies might sleep, but have you ever seen a drunk ladybug? I have. It walked up to a small drop of brandy on the table, sucked it up, stood up on his legs and tipped right over! True story!

1) "Do flies sleep? after prodding and tapping fruit flies, measuring their activity with ultrasound and infrared detectors, blasting them with sound waves and monitoring their genes, researchers at the Neurosciences Institute in San Diego have come to a definitive conclusion: the flies actually doze off in slumber patterns that are strikingly similar to those of humans.

Writing in the current issue of Science, the researchers report that the flies are somnolent mainly at night and active during daylight hours: that elderly (33-day-old) flies sleep less and more erratically than younger ones; that fruit flies deprived of sleep must nap longer to recover; that caffeine keeps them awake, and antihistamines make them that drowsy."
Source and further information:
http://www.time.com/.../0,9171,40744,00.html


2) ""Flies do most things that humans do—they eat, they sleep, they fight, they mate, they forage for food," Ganguly-Fitzgerald told LiveScience. Just as is often the case with humans, flies sleep a lot as young ones, sleep little as they get older, and "stay awake more after being fed caffeine and become sleepy in response to anti-histamine compounds," she said."
Source and further information:
http://www.msnbc.msn.com/id/14945525/

Don't they only live for 1 day or so? In that case, they would not need to sleep.

I'm no expert on the pests, but I'd say they don't. The problem,
though, is that sleep is not easy to define even in humans. We don't
understand what happens to our bodies when we sleep, how we sleep, or why
(although there are ideas about each of these). I think sleep is basically
defined as the unusual pattern in the electrical signals given off by the
brains of people who say (later) that they've been asleep. Kind of a
circular definition, eh? We can surmise that cats and dogs sleep because
they act like sleeping people --- lay down, close their eyes, don't
respond, snore and twitch when dreaming --- and they probably have similar
patterns in the electrical signals from their brains, though I don't know.
But with flies, now, they're so different that not seeing the same
behavior doesn't say much. Still, I'd say they don't because the most
convincing hypothesis I've heard about the reason for sleep is that it is
part of learning, and I've also heard that flies are capable of learning
anything at all. That's an argument, but by no means an answer

Hope I Helped!