The term negging seems to be widely misunderstood. The Freakonomics blog says:
Under particular discussion is a pickup technique that Mystery advocates known as "negging" — a move that involves interjecting an insult during an initial conversation with a woman. The motivation behind the insult is, as Esquire’s A.J. Jacobs puts it, to "lower her self-esteem, thus making her more vulnerable to your advances."
No, that is not correct. If the woman feels insulted, then negging won't work at all. The motivation for negging is to be flirtatious and playful without being rude.

The need for negging

A pick-up artist site defines:
Neg hits, or more commonly negs (short for “negative hits”), are quick, sometimes humorous remarks used by PUAs to get past the bitch shield of hot women. Many men, when approaching an HB, make the mistake of immediately lavishing them with compliments. This rarely ever works because it is a) not genuine, b) places the girl on a pedestal, and c) what every other guy does.

By negging a target, a PUA avoids falling into this trap. An example of a commonly used neg in the seduction community is: “Nice nails, are they real?” A comment like this accomplishes a number of things. First, it brings the woman (especially very attractive women, who are used to getting compliments) down a notch and shows that the PUA is not overawed by her beauty. Second, it creates a bit of a challenge, so, if the woman is at all interested, she will start chasing the PUA and trying to win his approval.

It is important to note that a neg hit is not an insult. Rather, it is an often humorous comment used to communicate active disinterest. New guys often make the mistake of insulting women or being mean to them. That is not the point of negs, and they should never be used to make women feel bad about themselves.

The goal of negging is to appease a woman’s hypergamous desire. The terminology from these dating coaches can be confusing, but men find it helpful for better relations with women.

Negging is just part of flirting

To understand flirting, you have to see how it is possible that more ambiguous communication can actually be better communication. When meeting someone new, it is just not possible to unambiguously define the relationship. You just don't have enough information. By making ambiguous statements, you are able to communicate a range of possibilities for how things might go, and get feedback. When both parties are flirting successfully, a lot of subtle info gets communicated.

Harvard Psychology professor Steven Pinker, whose new book is The Stuff of Thought, explains why people use ambiguous speech:

Pinker repeats that people often have to convey messages while unsure of their relationships. Indirect speech can minimize the risks in legal contexts with tangible costs (e.g. Bribes, threats). The same thing can happen in everyday life, because relationship mismatches have an emotional cost. Pinker emphasizes that indirect speech prevents individual knowledge from becoming mutual knowledge; mutual knowledge is the basis of our relationships. Humans think a lot about what others think about them, and their relationships are ratified by their mutual knowledge. As a result, to preserve their relationships (while transacting the business of their lives) humans often engage in hypocrisy and taboo.
Negging is a way of flirting, like double entendres. It is a useful way to teach men some simple flirting techniques. It is not meant to be taken too seriously.

Info for women

Many women also lack flirting skills, but help for them is readily available. Supermarkets are always selling magazines with tips for women in attracting men, and an attractive woman can usually get dates even without flirting skills. She can let a man approach her, and let him carry the conversation.

Some women will say that flirting is an annoying form of game-playing, and that negging in particular is just a practice of manipulative insults. Well, that is not really correct. Most men would rather be much more direct in their interactions with women. If you want to be more direct, then just skip the flirting, and you'll find that most men are happy to oblige.