A computer's dreams are not always of electric sheep, you know. As you mentioned, they have nightmares too! My iMac once told me that he was dreaming about being at a presentation. At some point, he suddenly realized that he didn't have his case on...His components were all exposed for everyone to see. Another time, my iMac mentioned that, in a dream, he was being stalked by Billy Gates....Who first tried to install Windows on him but when he refused, Billy then tried to rip out his motherboard. My poor iMac was freaked out.
But, yeah, I had similar problems to you about my iMac waking up. What I discovered is this: If a device or anything else communicating with my computer gets interrupted or has a change in status, the iMac will wake up in response. This could be if a printer turns off, there's a reconnection of a down network, a powered peripheral (like an iPod) turns itself off or is attached. You may have some settings stating to wake up the computer on network activity or device communication. It could be this or a number of other things.