Every night, I put my computer to sleep. Some mornings, I find that, for no discernible reason, my computer has turned itself on. It's not scheduled to turn on, and I don't know of any program that could be doing it. There's nothing in the system log that gives any hint; it shows essentially the same thing that it shows when I wake up my computer manually.
After scouring the net for an explanation, I found reports from people with similar problems. Somebody pointed out that you can sometimes (always??) wake up a computer by plugging in or unplugging a USB device. My keyboard is plugged in through a cheap hub; a loose connection might cause intermittent disconnects. One user on a forum somewhere (I've lost track of the original location) claims that his computer wakes up whenever he uses his microwave or other high-power device! He says that his electrical system is rather old, and suspects that the sudden power drain causes his computer to temporarily reduce power to his USB peripherals, which wakes the computer.
[robg adds: I had this issue with my old G5 and a really cheap USB hub, too. One night I disconnected all the USB peripherals and it slept just fine. The next day, I replaced the USB hub, and the machine no longer woke randomly overnight. (It was awake one morning when I went into the office, but the cat sleeping nearby on the desk told me exactly why the Mac had woken up!)]
Mac OS X Hints