I have an early 2009 24" iMac. Lately, when in sleep mode it will occasionally wake up for around ten seconds with the screen off, then go back to sleep. Wake on LAN is turned off so I can't figure out why this is happening!
There are a number of possible reasons, and the system actually logs the cause of each 'wake from sleep'.
Open a terminal and enter:
This may take some time to return a result, but when it does, you should get a series of lines that look something like the following:
Here are the possible 'Wake Reason' codes (lifted from OSXDaily)
A common reason for random wake-ups is network accesses.
If you go to System Preferences>Energy Saver, there you will see an option saying "Wake for network access". If this option is enabled, then your sleeping Mac will be able to wake-up for network accesses. For example, when you initiate a screen sharing from another Mac on your local network.
Anyway, this is all okay BUT when this option is enabled it's also documented on Apple's site that it will cause random wake-ups by just running the hard-drives but not starting up the screen; and it will go immediately back to sleep.
Also @macaco have putten it beautifully that you'll probably get a code for this reason.