I'm cheap so I have mine in a power strip and turn the strip off when I'm done. After of course I put it in standby.
I also wear a jacket around my apartment instead of cranking the heat up. So that tells you how cheap I am lol.
Instead of "cheap", you might describe yourself as environmentally responsible. You are using less power, and therefore are causing less pollution than if you cranked up the heat in your home and left things on all of the time.
Also, this leaves you with more money for other things. You could describe yourself as frugal or thrifty, or not wasteful.
When I think of someone being "cheap", I think about things like what is happening when someone goes to a restaurant and stiffs the waitress by not leaving a tip (in a country, like the U.S., where tips are expected; obviously, in countries where waitstaff are paid a livable wage without tips would be different). Or going to lunch with several people who order salads, while one eats lobster, and then suggesting that everyone just split the bill evenly. In other words, someone is "cheap" when they don't pay for something for which they should be paying.
To answer the initial question, I shut things off when I am not using them. It isn't so much the bill for the power, as the thought that I do not want to be responsible for another coal plant being built (or whatever other nasty thing would be done).
So, lsiberian, I think you are doing something too noble to be called "cheap". Even if it is only the money that is motivating you. After all, it isn't like saving this money is hurting others. It would be different if you were hurting others for money, but as it is, you are doing good for others for money. And there is nothing wrong with that.