I think that the issue is that you can't turn it on from being completely off in any other way than pushing the power button. You could use something like LogMeIn Ignition to turn it off, though.
Depending on your situation, it might be better just to let it sleep instead if you need to operate it remotely....Or pay a guy to sit in your house and wait for texts to telling him to turn it on and off, haha...
Edit: This comment is assuming that yours was sarcastic, which it seemed like, based upon the nature of the discussion above.
I'm looking for the best app for my iPhone 4s to turn on or off my iMac with Mountain Lion? I found one, Off remote, is there another one out there?
Why an app?
use this, I do, it's nice!
Wasting electricity that's why. Even sleep use some electricity.
I don't think I've turned off my G5 power-mac, my Windows XP/Vista/7, or my 2011 iMac in well. Whenever the power goes off?
Same. I haven't turned off a computer since my old 386SX, except (1) to move it, or (2) it wasn't responding to ctrl-alt-del / cmd-opt-esc.
The power draw of modern computers, especially when asleep, is very small. If you want to go nuts hunting down all your "vampiric power" and putting in hard switches on all of your electronics, I guess you can, but you'll probably spend more on the switches than you save on electricity.