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I have Mac mini with the latest Leopard + all patches. I've set it up for the monitor to go to sleep after 5 minutes of inactivity, but it just won't turn off.
The trouble started last week after I upgraded the RAM from 1gb to 2gb. Software-wise nothing changed.
Oddly enough, I have the same exact problem on my pc laptop. I suspected that the cat would just jump on the keyboard in the middle of the night and the monitor would wake up. But I locked the cat out of the computer room for the night and the monitor was still on in the morning. The cat denies all knowledge.

Clearly your cat can pick locks. Seriously though, the monitor won't enter sleep mode at all or does it goes to sleep and then just wake up before it should? – Bryan Schuetz – 2009-08-04T10:50:13.153