For any device, it is certainly best to power it down before removing power, as you stated. But once this is done, it really doesn't matter how quickly you remove the plug, only that you pull it straight out to avoid bending the prongs.
When you remove the plug, there is going to be a point where the connection is broken. No matter how slowly you remove the plug, when it hits that point, there is no more power, unless you have a high enough voltage to arc across the air gap.
As for projector bulbs, they might benefit from a gradual reduction in power, but you won't get that from removing the plug slowly; you get that from some special circuitry that can vary the power on power down or power up.
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possible duplicate of laptop: Should one plug the AC first or to the laptop first. And, to restate what I said as a comment in that question: It makes no difference. The AC/DC transformation is a one-way deal, so it literally doesn't matter (both circuits are electrically isolated from eachother - or at least they should be!).
– Breakthrough – 2012-05-09T03:47:03.300I don't think this is the same. I also think it does matter. You should connect the cord to the unit first, then plug it in to the outlet. Plugging a live cord into the unit is risky, although admittedly there's not much chance of a problem. But there's a right way and a wrong way to do everything, regardless of how much or how little risk there is of doing it wrong. Anyway, I don't see what difference the AC/DC transformation makes; you can shock yourself or cause a short circuit with either one, I know from experience during my electronic repair days long ago. – Marty Fried – 2012-05-09T04:04:34.713
@MartyFried are you seriously telling me there's a difference between the action of "connect the cord to the unit first" versus "plugging a live cord into the unit"? Unless you're using a cable with exposed conductors (in which case, you shouldn't be using it at all), there's no difference. Yes, there's a difference between shutting the device off (in which case, graceful termination is always best), but when you're plugging it in, no, there's no difference. – Breakthrough – 2012-05-09T04:13:52.533
@MartyFried define right way and wrong way, its a matter of opinion for everyone what is right or wrong. I suppose if you cannot pay attention you should not use electrical devices, or drive a car for that matter, that's my opinion. – Moab – 2012-05-09T15:11:12.583