This is a very apposite question, as the terms negative energy and positive energy get bandied about a lot, particularly with regard to social situations or the body, or unconventional therapeutic treatments using certain exotic substances or physical techniques.
The assumption is that negative energy is bad because that’s what we associate with the word “negative”. However, when you look at ionisers, for example, you’re struck by the fact that it is the positive ions, not the negative ones, that make you feel poorly, and that the negative ions are the ones you want to make the air feel fresh and invigorating. (See, for example,.)
Electricity, and electronics, too, is negative energy in the literal sense that it is a flow of negative particles called electrons—and yet it makes our modern-day lifestyle (including the computers that you and I are using right now) possible.
Which goes to show one should beware of applying everyday, value-judgement terms to scientific concepts. (Another classic one is the misinterpretation of the word relative in Einstein’s theories of relativity.) When you say negative energy to a scientist, they understand it in the scientific sense, which is quite different—as you can see from the other answers to this question—and devoid of the cultural associations we have with the word negative.